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Above we assumed that both directions of $T^2$ have the string size, so that its volume is of order $l_{IIA}^2$, as implied by eq.(REF). However, one could choose one direction much bigger than the string scale and the other much smaller. For instance, in the case of a rectangular torus of radii $r$ and $R$, $V_{T^2}=rR\sim l_{IIA}^2$ with $r\gg l_{IIA}\gg R$. This can be treated by performing a T-duality (REF) along $R$ to type IIB: $R\to l_{IIA}^2/R$ and $\lambda_{IIA}\to\lambda_{IIB}=\lambda_{IIA}l_{IIA}/R$ with $l_{IIA}=l_{IIB}$. One thus obtains: FORMULA which shows that the gauge couplings are now determined by the ratio of the two radii, or in general by the shape of $T^2$, while the Planck mass is controlled by its size, as well as by the 6d type IIB string coupling. The string scale can thus be expressed as [CIT] : FORMULA | 844 | hep-th/0102202 | 2,093,001 | 2,001 | 2 | 28 | false | true | 1 | UNITS |
We investigated the brane physics induced by a global monopole formed in three extra dimensions. The metric induced by the monopole background, with negative cosmological constant, makes the volume of the extra dimensions infinite. As usual in models of infinite extra dimensional volume, the graviton zero mode is not normalizable without a cut-off. We view a cut-off as physically natural, due to formation of adjacent defects during the dimension-reducing phase transition, and choose the cut-off radius to induce a hierarchical 4D Planck mass ($\sim 10^{18}$GeV) from a unified 7D Planck mass ($\sim$TeV). We have a possible range of parameters to make this cut-off radius (size of extra dimensions) consistent with current observations. | 741 | hep-th/0104067 | 2,136,279 | 2,001 | 4 | 6 | false | true | 2 | UNITS, UNITS |
Below the first Planck scale $E\ll E_{\rm Planck 1}=mc^2$, the energy spectrum of quasiparticles is linear, which corresponds to the relativistic field theory arising in the low-energy corner. At this Planck scale the "Lorentz" symmetry is violated. The first Planck scale $E_{\rm Planck 1}=mc^2$ also determines the convergence of the sum in Eq.(REF). In terms of this scale the Eq.(REF) can be written as FORMULA where $g=-1/c^6$ is the determinant of acoustic metric in Eq.(REF). This contribution to the vacuum energy has the same structure as the cosmological term in Eq.(REF). However, the leading term in the vacuum energy, Eq.(REF), is higher and is determined by both Planck scales: FORMULA | 700 | gr-qc/0104046 | 2,144,306 | 2,001 | 4 | 15 | false | true | 6 | UNITS, UNITS, UNITS, UNITS, UNITS, UNITS |
It is more convenient to work with Planck's unity. Natural unities are employed: $c = \hbar = 1$, $G = 1/\sqrt{M_P}$, $M_P$ being the Planck's mass whose value today is $M_{P0} = 1.221\times10^{19}GeV$. Hence, FORMULA where $M_{PR}$ is the value of the Planck's mass at the moment of the nucleosynthesis. | 304 | gr-qc/0105062 | 2,181,348 | 2,001 | 5 | 17 | true | false | 3 | UNITS, UNITS, UNITS |
In Figures REF and REF we show the difference power spectra for two maps at different observed wavelengths. We define $\delta T(\hbox{\boldmath $\theta$})=T^a(\hbox{\boldmath $\theta$})-T^b(\hbox{\boldmath $\theta$})$ and FORMULA A similar expression can be written for the polarization. The difference spectrum provides the new signature due to lithium, since the MAP or Planck satellites will measure with high precision the anisotropies at long photon wavelengths. | 467 | astro-ph/0105345 | 2,185,264 | 2,001 | 5 | 19 | true | false | 1 | MISSION |
In the present paper we shall set up a system of differential equations which consists of the RG equations for $G$ and $\Lambda$, the improved Einstein equations, an additional consistency condition dictated by the Bianchi identities, and the equation of state of the matter sector. This system determines the evolution of $G$, $\Lambda$, $a$, $\rho$ and $p$ as a function of the cosmological time $t$. We shall see that for $t \searrow 0$ all solutions to this system have a simple power law structure. This attractor-type solution fixes $\rho_{\rm tot}=\rho_{\rm crit}$ without any finetuning. If the matter system is assumed to obey the equation of state of ordinary radiation, the scale factor expands linearly, $a(t)\propto t$, so that the RG-improved spacetime has no particle horizon. For $t$ much larger than the Planck time the solutions of the RG-improved system approach those of standard FRW cosmology. | 914 | hep-th/0106133 | 2,221,552 | 2,001 | 6 | 15 | true | true | 1 | UNITS |
Indeed, as revealed by numerical analysis [CIT], regular gravitating monopoles exist only up to a maximal value $\alpha_{\rm max}$ of the coupling constant $\alpha$ (which is proportional the Higgs vacuum expectation value $v$ and the inverse Planck mass). Beyond $\alpha_{\rm max}$ the only solutions with unit magnetic charge are embedded abelian solutions, namely Reissner-Nordstrøm (RN) black hole solutions. Thus $\alpha_{\rm max}$ limits the domain of the EYMH parameter space, where non-abelian monopole solutions exist. | 527 | hep-th/0106227 | 2,232,534 | 2,001 | 6 | 25 | false | true | 1 | UNITS |
We estimate the column density and the mass of the [C II] emitting photodissociated gas using the results of the PDR model above. For the calculation we assume optically thin emission. The column density and mass is then given by: FORMULA where $\Omega$ is the area in steradian, $M_{\rm p}$ is the proton mass, $M_{\odot}$ is the mass of the sun, $D$ is the distance, $h$ is the Planck constant, $c$ is the vacuum speed of light, $A$ is the Einstein coefficient for spontaneous emission, $X_{\rm C^{+}} = 3 \times 10^{-4}$ is the abundance of ionized carbon, $g_{\rm u}$ and $g_{\rm l}$ are the statistical weights for the upper and lower level, $x_{\rm e} \approx 3 \times 10^{-4}$ is the ionization fraction, and $n_{\rm cr, H} = 3.5 \times 10^{3}$ is the mean critical density for collisions with atomic and molecular hydrogen. The density and the beam filling factors were taken from the PDR results (Table REF). In this calculation we assumed that all carbon is in singly ionized form and that the gas temperature is 200 K. For this gas temperature we assume a critical density for collisions with electrons of $n_{\rm cr, e} \approx 10$ cm$^{-3}$. This critical density is deduced from the collision strengths given by Blum & Pradhan (1992). | 1,248 | astro-ph/0107365 | 2,263,541 | 2,001 | 7 | 19 | true | false | 1 | CONSTANT |
The dynamics of $\chi$ is complicated. Even though $\chi$ has no effective mass during inflation, it has an effective quartic self coupling which determines its dynamics (see Eq. (REF)). The equations of motion in terms of the component fields $\chi_1,\chi_2$ are given by FORMULA We remind that $\chi_1$ and $\chi_2$ are the components of a a bulk field, therefore, they would have naturally taken initial values close to the fundamental scale in higher dimensions but close to the Planck scale in four dimensions. From the point of view of four dimensions, the fields simply roll down from the Planck scale because the self coupling induces a curvature terms for $\chi_1$ and $\chi_2$ fields. We note that the suppression in the couplings is very small $\sim (M_{\ast}/M_{\rm p})^2$ if $\kappa_2 \sim {\cal O}(1)$. The fields are very weakly self coupled. However, in the process of rolling down the potential their effective running mass becomes of $\sim H$, given by Eq. (REF). When this happens their dynamics is effectively frozen at a particular amplitude which observes the constraint derived independently in the earlier section, see Eq. (REF). | 1,153 | hep-ph/0108225 | 2,308,167 | 2,001 | 8 | 27 | true | true | 2 | UNITS, UNITS |
Crucially, the magnitude of $\Delta T/T$ is only logarithmically dependent on $t_{\rm in}$ and $t_*$. Using $1+z_{\rm ls}=1100$ and $1+z_{\rm eq}=2.4\times 10^4\Omega _0h_0^2,$ where $\Omega _0$ is the present total matter density of the universe in units of the critical density and $h_0$ is the Hubble parameter today in units of 100 km,s$^{-1}$,Mpc$^{-1}$, we find FORMULA The time $t_{\rm in}$ could reasonably be taken as the 5D Planck time $t_5$. By Eq. (REF) the 5D Planck mass is subject to $M_5\gtrsim 10^8$ GeV, so that $t_5\lesssim 10^{11}t_4$, where $t_4\approx 10^{-43}$ sec is the 4D Planck time. For $t_*\sim t_4\approx 10^{-43}$ sec and $t_{\rm in}\sim 10^{10}t_*$, the logarithmic term would be $\sim {1\over5}$, and is relatively insensitive to quite large changes in these quantities. Thus, using Eq. (REF), FORMULA This is a much tighter constraint on the initial anisotropy than obtained from nucleosynthesis, Eq. (REF). The observed large-angle temperature anisotropy in the CMB may have been contributed by bulk graviton effects in the very early universe if they have an initial amplitude of $\sim 10^{-3}\Omega _0h_0^2$. This anisotropy level is too low to have an observable effect on the output from primordial nucleosynthesis. | 1,254 | gr-qc/0108073 | 2,310,600 | 2,001 | 8 | 29 | true | true | 3 | UNITS, UNITS, UNITS |
Keeping in mind that the initial spatial size of the tori is Planck scale, it follows immediately from equation (REF) and from the time duration of the loitering phase that loitering lasts sufficiently long to allow causal communication over the entire spatial section. This is reflected in Fig. 5 which shows that the winding modes completely annihilate by the end of the loitering phase, after which $g(t)$ tends to a constant (Fig 6). | 437 | hep-th/0109165 | 2,338,245 | 2,001 | 9 | 20 | true | true | 1 | UNITS |
Let us analyse in some detail what happens if we choose a TeV for the string scale. This is about the lowest value which is just in agreement with experiments. (For a lower value massive string excitations should have shown up in collider experiments.) With $M_p \sim 10^{16} \mbox{TeV}$ we find FORMULA The Planck length is about $10^{-33} \mbox{cm}$ and hence in our units one TeV corresponds to $1/\left(10^{-18}\mbox{m}\right)$. Thus we obtain FORMULA For the case $p=8$ (one extra large dimension) we obtain that the perpendicular dimension is compactified on a circle of the size FORMULA Such a value is certainly excluded by observations. (In the next subsection we will compute corrections to Newton's law due to Kaluza-Klein massive gravitons and see that the size of the compact space should be less than a mm.) For $p=7$ we obtain (distributing the perpendicular volume equally on the two (extra large) dimensions) FORMULA This value is just at the edge of being experimentally excluded. The situation improves the more extra large dimensions there are. For example in the case $p=3$ (and again a uniform distribution of the perpendicular volume on the six dimensions ($V_\perp = R_\perp ^6$)) we obtain FORMULA which is in good agreement with the experimental value ($R_\perp ^{exp} =0... 0.1\mbox{mm}$). | 1,316 | hep-th/0110055 | 2,357,953 | 2,001 | 10 | 5 | false | true | 1 | UNITS |
The Sloan Digital Sky Survey (SDSS) is a joint project of The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Princeton University, the United States Naval Observatory, and the University of Washington. Apache Point Observatory, site of the SDSS telescopes, is operated by the Astrophysical Research Consortium (ARC). | 522 | astro-ph/0111058 | 2,400,498 | 2,001 | 11 | 2 | true | false | 2 | MPS, MPS |
The assumption $R \gg r$ does not seem to be impossible. It is motivated by the fact that in string theory the tree-level formula FORMULA between the Planck mass $M_{Pl}$ and the string scale $M_{str}$ receives large corrections. Therefore the relations $M_{str} \ll M_{Pl}$ and $R \sim M^{-1}_{str} \gg M^{-1}_{Pl} \sim r$ are not inconsistent with the string theory [CIT]. With this possibility in mind there were proposals of scenarios where part of the compact dimensions had relatively large size. For example, in a scenario shown in Fig. REF a physically interesting case corresponds to $R^{-1} \sim 10$MeV, $r^{-1} \sim 1$TeV. | 633 | hep-ph/0111027 | 2,400,878 | 2,001 | 11 | 2 | false | true | 1 | UNITS |
The spin $3/2$ gravitino occurs in supersymmetric theories as a superpartner of the graviton [CIT]. A massless gravitino only possesses $\pm 3/2$ helicity states. However, once supersymmetry is broken the gravitinos become massive, and they possess all four helicity states. Soon after realizing that the helicity $\pm 3/2$ states of a massive gravitino can be produced non-perturbatively [CIT], it was found out that the helicity $\pm 1/2$ states can also be produced from vacuum fluctuations [CIT]. They are produced even more abundantly compared to helicity $\pm 3/2$ states due to the Goldstino nature of helicity $\pm 1/2$ states which implies the absence of any Planck mass suppression in their couplings. | 711 | hep-ph/0111366 | 2,434,892 | 2,001 | 11 | 28 | false | true | 1 | UNITS |
In conclusion, we find that the formation of a bubble inside the false vacuum of an evolving scalar field freezes out the quantum fluctuations of the field. During the current epoch of cosmic acceleration, the scale of the horizon is $\sim 61$ orders of magnitude greater than that of a Planck--scale bubble that could begin to grow. If the largest quantum fluctuation within the horizon is sufficiently large, a critical bubble will form and expand to contain its future light cone. The largest fluctuation within our horizon is typically a $\sim 30$--$\sigma$ event, i.e. it is astronomically rare, but if this fluctuation is large enough to create an expanding bubble, then the fluctuation is frozen out and renders the universe highly inhomogeneous. | 753 | astro-ph/0111570 | 2,437,139 | 2,001 | 11 | 29 | true | true | 1 | UNITS |
If we consider a simple harmonic potential for the scalar field at values $\phi >\phi_{\rm c}$ and take the density of the flat universe today to be $30\%$ matter and $70\%$ vacuum energy, we find through a numerical integration that the scalar field reaches the potential minimum after $\sim 92$ $e$-folds. Looking back in time from the moment of recollapse, the value of $\vert\langle\phi\rangle-\phi_{\hbox{\rm \scriptsize c}}\vert$ at the beginning of the final $e$-fold is $3\%$ of $M_{\hbox{\rm \scriptsize Pl}}$. If the potential is too steep a bubble will form within the past light cone and will be able to envelope the entire Hubble volume before the scalar potential reaches its minimum. For the scalar field to roll rather than tunnel, the slope past the cliff is bounded by FORMULA This limit cannot be evaded without increasing the rate of change of $\phi$, which would reduce the number of $e-$foldings before the field reaches the minimum. As $\langle\phi\rangle$ approaches the potential minimum, more bubbles could form and expand if the depth of the potential minimum is not too small. The formation of these bubbles destroys the homogeneity of the causally connected patch of the universe. In the cyclic universe the expansion will decelerate about one billion years before the potential reaches its minimum, because at this time the kinetic energy of the field begins to dominate the potential energy. Based on a numerical integration of the evolution equation for $\phi$, we find that expanding bubbles will form at this stage unless FORMULA This constraint requires fine-tuning since the generic value of the slope lies in the Planck regime. | 1,664 | astro-ph/0111570 | 2,437,142 | 2,001 | 11 | 29 | true | true | 1 | UNITS |
In the present paper we shall explore the connection between the dispersion relation and the statistical mechanics of Hawking quanta. We shall first work out general expressions in Section REF which we then apply to both the canonical picture and the better sound microcanonical picture in Section REF. The starting point of the latter approach is the idea that black holes are (excitations of) extended objects ($p$-branes), a gas of which satisfies the bootstrap condition [CIT]. This yields a picture in which a black hole and the particles it emits are of the same nature and the statistical mechanics of the radiation then follows straightforwardly from the area law of black hole degeneracy [CIT]. One obtains an improved law of black hole decay which is consistent with unitarity (energy conservation) and no information loss paradox is expected. In fact, black holes approximately decay exponentially in this picture, although departures from the canonical behavior occur only around (or below) the planck mass [CIT]. | 1,025 | hep-th/0111287 | 2,440,811 | 2,001 | 11 | 30 | false | true | 1 | UNITS |
After the extremely accurate CMB spectrum measurement by the COBE satellite in 1989, proving that the radiation was a perfect blackbody [CIT], and the first detection of deviations [CIT] from the perfect homogeneity at the level of 10$^{-5}$ K, most experiments have concentrated on improving the measurement of the anisotropies. In most theories and with consistent available data, the statistical distribution of the CMB anistropies is Gaussian. The anisotropies are therefore represented by their spherical harmonic power spectrum (non-Gaussianity is nevertheless looked for). The most accurate results are from COBE on large angular scale ($>$ 7 degrees) and on small angular scales ($<$ 2 degrees) from Boomerang [CIT], Maxima [CIT], and DASI [CIT] (see Figure REF). The intermediate angular scales, between COBE and the other experiments, lack measurements, due to the small sky coverage of these experiments. The main Archeops goal is to link COBE and Boomerang-Maxima-DASI angular scales, with high-sensitivity detectors covering a large fraction of sky (30% of the sky). Archeops is also a testbed for Planck-HFI, using the same type of cryogenic system and detectors; and it measures dust and galactic sources in a polarized frequency band. | 1,250 | astro-ph/0112205 | 2,451,313 | 2,001 | 12 | 9 | true | false | 1 | MISSION |
We have applied our procedure to a flare on YZ CMi observed during a coordinated run involving telescopes at the South African Astronomical Observatory, and the ESA X-ray satellite, EXOSAT, on 4 March 1985. The photometric observations consisted of UBVRI photometry with a 0.75-m telescope. Details have been published by [CIT]. The spectra of the flare on YZ CMi, over the wavelength range 3600--4400Å, were analysed by [CIT] using a gas-dynamic model. Based on the gas-dynamic model and using the data set for the flare observed by [CIT] on YZ CMi, [CIT] derived the main physical parameters at flare maximum. They matched quite well the observed data with the theoretical decrement for a temperature $T=10^{4} \rm{K}$, electron density $10^{14} \rm{cm^{-3}}$ and optical depth of the layer at the $Ly\alpha$ line center $\tau_{Ly\alpha}=2,10^{6}$. They also derived the emitting source area of $>5$x$10^{17} \rm{cm^{2}}$ using a description of the optical continuum as a Planck function for a temperature of $10^{4} \rm{K}$. | 1,027 | astro-ph/0112224 | 2,451,959 | 2,001 | 12 | 10 | true | false | 1 | LAW |
More important are the changes in the electroweak scale $v$, which are tied to the scale of supersymmetry breaking in most supersymmetric models. For example, in the traditional supergravity mediated models there are various soft supersymmetry breaking masses (scalar masses, sfermion masses, and other bilinear and cubic scalar terms), which are usually assumed to have the same order of magnitude $m_{soft}$ at the Planck scale.[^5] Although these soft parameters run (and may change sign for scalar mass-squares), they are generally of the same order of magnitude at the weak scale. Typically, one finds that $v^2$ (and the inverse $G_F^{-1}$ of the Fermi constant) scales as $m_{soft}^2/\alpha_{weak}$, where $\alpha_{weak} = \frac{3}{5} \alpha_1 + \alpha_2$, and that the corresponding $W$ and $Z$ masses scale as $m_{soft}$. The underlying mechanism for breaking supersymmetry in the hidden sector and therefore generating $m_{soft}$ is unknown. We shall parametrize our ignorance by introducing FORMULA Then, FORMULA | 1,024 | hep-ph/0112233 | 2,463,687 | 2,001 | 12 | 17 | true | true | 1 | UNITS |
In general, it might be too strict a requirement to demand that all of the required features appear at the renormalizable level. In many string models the renormalizable Yukawa couplings are either unknown or are 0,1 (e.g. Type I models). Thus, to reproduce the observed fermion masses, non-renormalizable operators must be taken into account. The mass hierarchy is then created via powers of a small (in Planck units) VEV of a certain field $\phi$ [CIT], i.e. FORMULA Here $q_{\alpha\beta\gamma}$ is integer and can sometimes be associated with a $U(1)$ charge (as in the Froggatt-Nielsen mechanism). Clearly, if this field breaks supersymmetry, $F_{\phi}\not=0$, the generated A-terms will be nonuniversal: FORMULA Generally, $\phi$ is expected to give a (small) contribution to supersymmetry breaking. To estimate its natural size, let us recall that the Kähler potential for untwisted fields is given by $K=-\ln(S+\bar S)-3 \ln(T+\bar T- \phi \bar \phi)$. The resulting auxiliary field is then FORMULA A similar result holds for a twisted $\phi$. For small $\phi$, $F_{\phi}$ is typically of order $\phi m_{3/2}$ (see also e.g. [CIT]). As a result, the Yukawa-induced contribution to the A-terms is FORMULA The "charges" $q_{\alpha\beta\gamma}$ are generation-dependent and order one, so the resulting non-universality is very significant. Again, we come to the conclusion that realistic models of the fermion masses entail non-universal A-terms. We note that additional nonuniversal contributions may come from the Kähler potential. However, these are not direcly related to the Yukawa structures, so we do not discuss them here. | 1,634 | hep-ph/0112260 | 2,468,111 | 2,001 | 12 | 19 | false | true | 1 | UNITS |
Experimental signals due to effects in these kinds of theories are expected at the Planck scale, $M_{\rm Pl} = \sqrt{\hbar c/G} \simeq 10^{19}$ GeV, where particle physics meets up with gravity. This energy scale is inaccessible in accelerator experiments. However, a promising apprach has been to adopt Lorentz and CPT violation as a candidate signal of new physics originating from the Planck scale. The idea is to search for effects that are heavily suppressed at ordinary energies, e.g., with suppression factors proportional to the ratio of a low-energy scale to the Planck scale. Normally, such signals would be unobservable. However, with a unique signal such as Lorentz or CPT violation (which cannot be mimicked in conventional physics) the opportunity arises to search for effects originating from the Planck scale. This approach to testing Planck-scale physics has been aided by the development of a consistent theoretical framework incorporating Lorentz and CPT violation in an extension of the standard model of particle physics. [CIT] In the context of this framework, it is possible to look for new signatures of Lorentz and CPT violation in atomic and particle systems that might otherwise be overlooked. | 1,220 | hep-ph/0112318 | 2,474,428 | 2,001 | 12 | 23 | false | true | 5 | UNITS, UNITS, UNITS, UNITS, UNITS |
Supersymmetry (${\cal N}=1$) has been applied to phenomenology in the last two decades due to the fact that quadratic divergences which may destabilize the hierarchy of scales are canceled. It is of obvious interest the search for ${\cal N}=0$ theories in which there is some level of suppression of quadratic divergences. In particular, it has been recently realized that the scale of fundamental physics could be anywhere between, say 1-TeV and the Planck scale $M_p$ [CIT]. The largeness of the Planck scale would then be an artifact of the presence of large extra dimensions or warp factors of the metric [CIT]. Thus it has been put forward the idea that the weak scale could be associated to the string scale [CIT]. On the other hand the SM works so well that it is difficult to make the string scale lighter than a few TeV without entering into conflict with experimental data (see e.g. ref. [CIT] for a nice physical view of the problem). Furthermore, the absence of any exotic source of flavour changing neutral currents (FCNC) would be most easily guaranteed if the string scale was postponed to scales of order 10-100 TeV. But if one has $M_s\sim 10-100$ TeV, we will have to explain the relative smallness of the weak scale $M_Z=90$ GeV compared to the string scale. This we call the "modest hierarchy problem". | 1,322 | hep-th/0201205 | 2,508,266 | 2,002 | 1 | 25 | false | true | 2 | UNITS, UNITS |
The guiding intuition came in part from research in quantum gravity where it is often assumed that the Planck length $L_p$ has a fundamental role in the short-distance structure of space-time. Such a structural role for the Planck length can easily come into conflict with one of the cornerstones of Einstein's Special Relativity: FitzGerald-Lorentz length contraction. According to FitzGerald-Lorentz length contraction, different inertial observers would attribute different values to the same physical length. If the Planck length only has the role we presently attribute to it, which is basically the role of a coupling constant (an appropriately rescaled version of the gravitational coupling), no problem arises for FitzGerald-Lorentz contraction, but if we try to promote $L_p$ to the status of an intrinsic characteristic of space-time structure it is natural to find conflicts with FitzGerald-Lorentz contraction. For example, it is very hard (perhaps even impossible) to construct discretized versions or non-commutative versions of Minkowski space-time which enjoy ordinary Lorentz symmetry.[^1] Therefore, unless the Relativity postulates are modified, it appears impossible to attribute to the Planck length a truly fundamental (observer-independent) intrinsic role in the microscopic structure of space-time. | 1,322 | hep-th/0201245 | 2,514,096 | 2,002 | 1 | 30 | false | true | 4 | UNITS, UNITS, UNITS, UNITS |
To clarify the probabilistic interpretation of the RGE (REF), we start by recalling the simplest example of a stochastic process, namely the Brownian motion of a small particle in a viscous liquid and in the presence of some external force, like gravitation [CIT]. The particle is so small that it can feel the collisions with the molecules in the liquid; after each such a collision, the velocity of the particle changes randomly. And the liquid is so viscous that, after each collision, the particle enters immediately a constant velocity regime in which the friction force $\propto v^i$ (with $v^i$ the velocity of the particle) is equilibrated by the random force due to collisions together with the external force $F^i(x)$. In these conditions, the particle executes a random walk whose description is necessary statistical. The relevant quantity is the probability density $P(x,t)$ to find the particle at point $x$ at time $t$. This is normalized as: FORMULA and obeys an evolution equation of the diffusion type, known as the Fokker-Planck equation [CIT] : FORMULA Here, $D$ is the diffusion coefficient, which is a measure of the strength of the random force; for simplicity, we assume this to be a constant, i.e., independent of $x$ or $t$. The solution to eq. (REF) corresponding to some arbitrary initial condition $P(x,t_0)$ can be written as FORMULA where $P(x,t|x_0,t_0)$ is the solution to (REF) with the initial condition: FORMULA Physically, this is the probability density to find the particle at point $x$ at time $t$ knowing that it was at $x_0$ at time $t_0$. | 1,581 | hep-ph/0202270 | 2,550,436 | 2,002 | 2 | 27 | false | true | 1 | FOKKER |
The persistence of the kinematic curvature statistics in the face of nonlinear effects can also be understood in these terms. Essentially, the tail of the curvature PDF remains unaffected by the back reaction because it describes areas of anomalously large curvature ($K\gg k_{\nu}$) where, due to the anticorrelation property, the field is weak. On a slightly more quantitative level, we argue that the effect of the back reaction on the curvature can also be modelled by a simple nonlinear relaxation term, as in Eq. (REF): FORMULA Here $\tau_r^{-1}(B)$ is again estimated via Eqs. (REF) and (REF). The nonlinear relaxation term in Eq. (REF) is then FORMULA where ${\hat {\bf n}}={\bf K}/K$. With this correction, the Fokker--Planck equation (REF) for the PDF of curvature becomes FORMULA where ${\alpha}$ is a numerical constant of order unity and, as before, $K$ is rescaled by $K_*\sim k_{\nu}$. It is a straightforward exercise to show that the stationary PDF is now given by FORMULA which has the same power tail $\sim K^{-13/7}$ as its kinematic counterpart (REF). | 1,072 | astro-ph/0203219 | 2,568,530 | 2,002 | 3 | 14 | true | false | 1 | FOKKER |
The situation is very different if one considers the supersymmetric (SUSY) extension of the Standard Model. Existence of superparticles allows gauge invariant dimension five operators which can induce nucleon decay after superparticle dressing [CIT].[^3] These operators are very dangerous because they are suppressed only by a single power of the Planck mass. In fact, for the superparticle masses around 1 TeV, present proton decay experiments constrain the mass scale of the dimension five operators much larger than the Planck mass, or in other words, their coefficients should be much smaller than unity when normalized by the Planck scale. This is indeed embarrassing if one believes the widely accepted argument on the generality that all operators which are allowed by symmetry should arise with order one coefficients. There are many attempts to explain the smallness of these generic dimension 5 operators. They include 1) imposing some symmetry such as the family symmetry [CIT], the discrete gauge symmetry [CIT], the Peccei-Quinn symmetry [CIT], the U$(1)_A$ symmetry [CIT] and the $R$ symmetry [CIT], and 2) attributing to configurations of quarks and leptons in extra spatial dimensions [CIT]. | 1,208 | hep-ph/0203192 | 2,576,729 | 2,002 | 3 | 20 | false | true | 3 | UNITS, UNITS, UNITS |
In this paper we apply the techniques developed in S01 to realistic simulations of the TOD coming from one of the 30GHz Planck LFI's channels. In section [2] we summarize some of the conclusions of S01 and present the semi-analytic adaptive filter that should be used in a realistic case. Section [3] describes the simulations used in this work. In section [4] we describe the analysis of the simulated data. In section [5] we describe the performance of the optimal adaptive filter, comparing it with other filtering schemes such as Gaussian filter and MHW. Finally, in section [6] we discuss our conclusions and give an outline of future work in this field. | 659 | astro-ph/0203485 | 2,585,092 | 2,002 | 3 | 27 | true | false | 1 | MISSION |
We review certain emergent notions on the nature of spacetime from noncommutative geometry and their radical implications. These ideas of spacetime are suggested from developments in fuzzy physics, string theory, and deformation quantisation. The review focuses on the ideas coming from fuzzy physics. We find models of quantum spacetime like fuzzy $S^4$ on which states cannot be localised, but which fluctuate into other manifolds like $CP^3$. New uncertainty principles concerning such lack of localisability on quantum spacetimes are formulated.Such investigations show the possibility of formulating and answering questions like the probabilty of finding a point of a quantum manifold in a state localised on another one. Additional striking possibilities indicated by these developments is the (generic) failure of $CPT$ theorem and the conventional spin-statistics connection. They even suggest that Planck's " constant " may not be a constant, but an operator which does not commute with all observables. All these novel possibilities arise within the rules of conventional quantum physics,and with no serious input from gravity physics. | 1,145 | hep-th/0203259 | 2,586,441 | 2,002 | 3 | 27 | false | true | 1 | CONSTANT |
The differential cross sections $d\sigma/d\mbox{$M_{\rm BH}$}$ for the BH produced at the LHC and a 200 TeV VLHC machines are shown in Figs. REFb and REFf, respectively, for several choices of $M_P$. The total production cross section at the LHC for BH masses above $M_P$ ranges from 0.5 nb for $\mbox{$M_P$}= 2$ TeV, $n=7$ to 120 fb for $\mbox{$M_P$}= 6$ TeV and $n=3$. If the fundamental Planck scale is $\approx 1$ TeV, the LHC, with the peak luminosity of 30 fb$^{-1}$/year will produce over $10^7$ black holes per year. This is comparable to the total number of $Z$'s produced at LEP, and suggests that we may do high precision studies of TeV BH physics, as long as the backgrounds are kept small. At the VLHC, BHs will be produced copiously for their masses and the value of the fundamental Planck scale as high as 25 TeV. The total production cross section is of the order of a millibarn for $\mbox{$M_P$}= 1$ TeV and of order a picobarn for $\mbox{$M_P$}= 25$ TeV. | 972 | hep-ph/0204031 | 2,592,490 | 2,002 | 4 | 3 | false | true | 2 | UNITS, UNITS |
To our knowledge, assumptions (2) and (3), which underlie the derivation of the Fokker-Planck equation from the Boltzmann equation [CIT], are shared by all methods aimed at simulating the relaxational evolution of stellar clusters and all of them also rely on spherical symmetry, with the exception of the code developed by [CIT] which allows overall cluster rotation (see paper I for a short review of these various methods). We have based our code on the Monte Carlo (MC) scheme invented by Hénon [- [CIT]; - [CIT]; - [CIT]; - [CIT]]. The reason for this choice, presented in detail in paper I, is basically that this algorithm offers the best balance between computational efficiency, with CPU time scaling like $N_\mathrm{p}\ln(cN_\mathrm{p})$ where $N_\mathrm{p}$ is the number of particles and $c$ some constant, and the ease and realism with which physics beyond relaxation, in particular stellar collisions, can be incorporated. Other codes stemming from Hénon's scheme have been developed and very successfully adapted to the dynamics of globular clusters [CIT] but we are not aware of any previously published adaptation of this method to the realm of galactic nuclei. | 1,178 | astro-ph/0204292 | 2,609,342 | 2,002 | 4 | 17 | true | false | 1 | FOKKER |
A recent proposal of lowering the fundamental Planck scale to the TeV range has provided a new perspective on studying black hole formation in ultra-relativistic collisions [CIT]. It has been argued that in particle collisions with energies above the Planck scale $M_D$ ($M_D \sim$ TeV), black holes can be produced and their production and decay can be described semiclassically and thermodynamically [CIT]. In proton-proton collisions at the Large Hadron Collider (LHC) at CERN with center of mass energy of several TeV, for example, the distinctive characteristics of black hole production would be large multiplicity events [CIT]. The event rates depend strongly on the ratio of the minimum mass of the black hole and the Planck scale and to a lesser extent on the number of extra dimensions [CIT]. Recently it has also been pointed out that cosmic ray detectors sensitive to neutrino induced air showers, such as large Pierre Auger Observatory, could detect black holes produced in the neutrino interactions with the atmosphere [CIT], for example, from interactions of the cosmogenic neutrinos produced in interaction of cosmic rays with the cosmic microwave background. If interactions are not detected, then cosmic ray detectors could provide constraints on the fundamental Planck scale for any number of extra dimensions [CIT]. | 1,335 | hep-ph/0204218 | 2,611,475 | 2,002 | 4 | 18 | true | true | 4 | UNITS, UNITS, UNITS, UNITS |
Nevertheless, in theories with extra compact dimensions the situation is on the opposite. In those models SM particles are assume to live on a four dimensional hypersurface (the brane) embedded in a higher dimensional space (the bulk). The extra dimensions are here taken to be compactified on a flat manifold [CIT]. These theories have been motivated by the possibility of having a small fundamental scale for quantum gravity. The aftermath of such constructions is the reduction of the energy scale cut-off that suppresses all non renormalizable operators that involve SM particles, as for instance the dimension 5 operator that gives a Majorana mass to the neutrino: FORMULA The physical meaning of the scale $\Lambda$ depends on the nature of the compactification as well as on the physics that generates such an operator. In theories with flat extra dimensions, $\Lambda\leq M$, where $M$ is the fundamental scale at which gravity becomes strong, that related to the effective Planck scale $M_P$ and the volume of the n-th dimensional extra compact space, $V_n$, by the relationship [CIT] : $M^{n+2} V_n = M_P^2$. Current limits indicate that $M$ could be as low as few TeV [CIT]. | 1,185 | hep-ph/0205173 | 2,649,103 | 2,002 | 5 | 15 | false | true | 1 | UNITS |
A class of anomalous diffusions are currently described through the non-linear Fokker-Planck equation (NLFPE) FORMULA where $D$ and $J$ are the diffusion and drift coefficients, respectively. Tsallis and Bukman [CIT] have shown that, for linear drift, the time dependent solution of the above equation is a Tsallis-like distribution with $q=1+\mu-\nu$. The norm of the distribution is conserved at all times only if $\mu=1$, therefore we will limit the discussion to the case $\nu=2-q$. | 486 | nucl-th/0205044 | 2,651,500 | 2,002 | 5 | 16 | false | true | 1 | FOKKER |
where $\nu_{o}$ and $\nu_{r}$ are the observed and rest frame frequencies respectively, $S_{\nu_{o}}$ is the flux in the observed frame, $B(\nu_{r},T_{dust})$ is the Planck function in the rest frame and $T_{dust}$ is the dust temperature. The gas mass is then obtained by assuming a fixed gas to dust ratio. For the most extreme *IRAS* galaxies, the best current estimate of the gas to dust ratio is $540\pm290$ [CIT]. For comparison, the gas to dust ratio in spiral galaxies is thought to be $\sim500$ [CIT], and $\sim700$ in ellipticals [CIT]. The mass absorption coefficient in the rest frame, $\kappa_{r}$, is taken to be: | 627 | astro-ph/0205422 | 2,662,200 | 2,002 | 5 | 24 | true | false | 1 | LAW |
Recently, a model involving both a $SO(3)$ triplet of Higgs fields as well as an $O(3)$ triplet of Goldstone field was considered in [CIT]. Coupling the Lagrangian of this model to gravity, the authors were able to construct finite mass solutions incorporating both the gravitating monopole of [CIT] and the global monopole of [CIT]. Because many features of these solutions were left open, we reconsider here the classical equations and put the emphasis on several unsolved questions, namely : (i) how does the topological defect emerge from the purely gravitating magnetic monopole, (ii) what is the domain of existence of the solutions in the space of the parameters, (iii) do the solutions bifurcate into black holes solutions, (iv) do these features persist for large values of the self-interacting coupling constant. These questions are worth studying because it is known that the global monopole has a much stronger gravitational field at large distances as compared to that of the local monopole. The reason for this is that the space-time of the global monopole is not asymtotically flat, while that of the gauged monopole is. However, at short distances the gravitational effects of the global monopole are weak as long as its mass is much smaller than the Planck mass [CIT]. On the other hand, it is well known that local monopoles stop to exist when their radius becomes comparable to the corresponding Schwarzschild radius, which implies that the mass of the monopoles is of order of the Planck mass [CIT]. Since we are studying critical phenomena of these monpoles, the mass of both the local and the global monopole are of the order of magnitude of the Planck mass and the argument that the short distance gravitational field of the global monopole is weak doesn't hold anylonger. One might thus expect significant changes of the critical behaviour of the local monopole in the spacetime of a global one. | 1,919 | hep-th/0206004 | 2,674,169 | 2,002 | 6 | 3 | false | true | 3 | UNITS, UNITS, UNITS |
A refinement of the present analysis for the determination of $f_k$ will be pursued in the future by software simulations of the radiometer functions to accurately study the combined effect of all components. Finally, laboratory measurements of a prototype radiometer working under conditions close to those of Planck mission constitute the most important checks for the ultimately understanding of the behaviour of Planck LFI radiometers regarding the $1/f$ type noise and possible further effects. Results of preliminary laboratory measurements performed of Planck-LFI prototype radiometers will be presented in forthcoming publications. | 639 | astro-ph/0206093 | 2,678,364 | 2,002 | 6 | 6 | true | false | 3 | MISSION, MISSION, MISSION |
Excess of the high energy CR electrons in the halo region, indicated by the flat spectrum, strongly suggests the particle acceleration in an intracluster space. Models considering particle acceleration by intracluster magnetic turbulence were discussed by Roland (1981), Schlickeiser, Sievers, & Thiemann (1987), and Petrosian (2001). In this paper, we model the radio halo in terms of particle acceleration by the intracluster turbulent magnetic fields. The turbulence is assumed to be an ensemble of Alfvén waves, and the CR electrons are accelerated by pitch angle scattering by the Alfvén waves. Distribution functions of the CR electrons in energy space are obtained by solving a Fokker-Planck equation for the assumed turbulent spectra with various power indices. The calculated radio spectra are compared with the observed one to determine the energy spectrum of the turbulent Alfvén waves. | 897 | astro-ph/0206269 | 2,690,901 | 2,002 | 6 | 17 | true | false | 1 | FOKKER |
The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, the University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington. | 549 | astro-ph/0206293 | 2,691,736 | 2,002 | 6 | 17 | true | false | 2 | MPS, MPS |
Here we have introduced the Planck scale $\Lambda$ since a length parameter is needed in order to tie objects of different dimensionality together: 0-loops, 1-loops,\..., $p$-loops. Einstein introduced the speed of light as a universal absolute invariant in order to "unite" space with time (to match units) in the Minkwoski space interval: FORMULA A similar unification is needed here to "unite" objects of different dimensions, such as $x^\mu$, $x^{\mu \nu}$, etc\... The Planck scale then emerges as another universal invariant in constructing an extended scale relativity theory in C-spaces [2]. | 599 | hep-th/0206181 | 2,697,309 | 2,002 | 6 | 19 | false | true | 2 | UNITS, UNITS |
By exploiting the factorized structure of $W_n[\alpha]$, Eq. (REF), one can verify that $Z_n[U]$ satisfies a recurrence formula similar to Eq. (REF), that is, FORMULA and the elementary propagator $Z_\epsilon[U|U_{n-1}]$ is given by an equation analogous to Eq. (REF): FORMULA Note that for fixed $U_{i-1}$, the probability ${\cal P}_i[\alpha]$ is in fact a function of $\alpha_i$ given by Eqs. (REF) and (REF). We expect $Z_\epsilon[U_i|U_{i-1}]$ to differ from unity by terms which vanishes as $\epsilon\to 0$. In fact the deviation is of order $\epsilon$, as we now show. To proceed, we note that the weight function ${\cal P}_i[\alpha]$ is a Gaussian of width $\epsilon$ in the variable $\epsilon\alpha$, and we perform an expansion of the group $\delta$-function in Eq. (REF) up to quadratic order in $\epsilon\alpha_i\sim \sqrt{\epsilon}$. To perform this expansion, we apply the identity (REF) derived in Appendix and obtain, in direct generalization of Eq. REF) and performing the integral over $\alpha_i$, we finally arrive at FORMULA The steps needed to obtain the equation satisfied by $Z_\tau[U]$ in the continuum limit are now identical to those leading to the Fokker-Planck equation (REF). Reinstating coordinate dependence, one gets FORMULA which is Eq. (REF). | 1,275 | hep-ph/0206279 | 2,706,832 | 2,002 | 6 | 26 | false | true | 1 | FOKKER |
We study the effect of imperfect subtraction of the Sunyaev-Zel'dovich effect (SZE) using a robust and non-parametric method to estimate the SZE residual in the Planck channels. We include relativistic corrections to the SZE, and present a simple fitting formula for the SZE temperature dependence for the Planck channels. We show how the relativistic corrections constitute a serious problem for the estimation of the kinematic SZE component from Planck data, since the key channel to estimate the kinematic component of the SZE, at 217 GHz, will be contaminated by a non-negligible thermal SZE component. The imperfect subtraction of the SZE will have an effect on both the Planck cluster catalogue and the recovered CMB map. In the cluster catalogue, the relativistic corrections are not a major worry for the estimation of the total cluster flux of the thermal SZE component, however, they must be included in the SZE simulation when calculating the selection function and completeness level. The power spectrum of the residual at 353 GHz, where the intensity of the thermal SZE is maximum, does not contribute significantly to the power spectrum of the CMB. We calculate the non-Gaussian signal due to the SZE residual in the 353 GHz CMB map using a simple Gaussianity estimator, and this estimator detects a 4.25-sigma non-Gaussian signal at small scales, which could be mistaken for a primordial non-Gaussian signature. The other channels do not show any significant departure from Gaussianity with our estimator. | 1,520 | astro-ph/0207178 | 2,722,573 | 2,002 | 7 | 9 | true | true | 4 | MISSION, MISSION, MISSION, MISSION |
We can obtain a more restrictive condition by requiring that the curvature is small everywhere up to the formation of the closed trapped surface [CIT]. This is only possible if we leave the Aichelburg-Sexl limit of the metric, which describes an infinitely boosted particle of zero size [CIT], and instead consider particles of finite size r [CIT]. In this case the maximum curvature in Planck units is given by FORMULA The impact parameter of the collision is given by $b \sim J/E$, and the particle size r must be less than $b$. This leads to the requirement that $E << M_{\rm Planck} J^{2/3}$, or equivalently that the range of validity of the semi-classical approximation for fixed J is FORMULA Clearly, only processes with large J can be described semi-classically. | 770 | gr-qc/0207078 | 2,740,177 | 2,002 | 7 | 21 | false | true | 2 | UNITS, UNITS |
This leads to the the following succinct form of dynamical field equations which describe the degree of freedom corresponding to transverse and longitudinal components, FORMULA where FORMULA We can easily see, reducing the equation into this form, eqn(REF) describing the transverse component of gravitino $\psi_i^T$ is decoupled from the longitudinal gravitino component, and its coupling to the other fields are Planck mass suppressed. So we hereafter pay our attention to the equation which describes the longitudinal component of gravitino, eqn(REF). The form of $\Upsilon$ in (REF) tells us that, in the absence of Kähler terms which mix the various left chiral superfields, we need only worry about the fermionic partners of dynamical scalar fields. Furthermore, for our superpotential, there is no mixing between the fermion associated with $\phi_1$ and those of $\phi_2$ and $\phi_3$, as long as $\phi_2=\phi_3=0$ which is true because they stay at the origin due to R-symmetry once they roll down to the origin during the inflation. Thus, even though the effective masses of the fermions corresponding to $\phi_2$ and $\phi_3$ are changing, those fermions do not contribute to the goldstino and we can concentrate on the evolution of the other fields for the purpose of our calculation. | 1,295 | hep-ph/0208276 | 2,790,827 | 2,002 | 8 | 30 | false | true | 1 | UNITS |
A priori, one would think that this observation is not useful for working out the consequences that GUT symmetry imply for 4D observers, which only have experimental access to the correlators of bulk field zero modes. However, the Planck correlators become indistinguishable from the Green's functions of zero modes as the external momenta are lowered below the KK mass gap. It follows from this that there is a calculable relation between the UV couplings of the bulk theory (as defined through Planck observables) and the parameters measured at low energy. Consequently, high energy GUT symmetry in an AdS$_5$ background compactified by branes makes definite predictions for low energy data. | 693 | hep-ph/0209158 | 2,811,525 | 2,002 | 9 | 16 | false | true | 2 | OTHER, OTHER |
Finally, modified dispersion relations for matter probes have been recently [CIT] argued to characterise flat space theories in certain models in which the Planck "length" is considered a real length. As such it should be transformed under usual Lorentz boosts. The requirement that the Planck length be, along with the speed of light, also *observer independent* leads quite naturally to modified "Lorentz transformations", and also to modified dispersion relations for particles. This approach is termed "Doubly Special Relativity" (DSR) [CIT]. The DSR approach should be distinguished from the other approaches, mentioned so far, where the Planck length scale is associated to a 'coupling constant' of the theory, and thus is observer independent by definition. This is clearly the case of Einstein's General Relativity, where the Planck scale is related to the universal gravitational coupling constant (Newton's constant), and in string theory (critical and non-critical), where the Planck length is related to the characteristic string scale of the theory, which is also independent of inertial observers. | 1,111 | hep-th/0210079 | 2,845,637 | 2,002 | 10 | 8 | false | true | 5 | UNITS, UNITS, UNITS, UNITS, UNITS |
We can easily match the predicted value, $\approx 2\rho_{\rm d}$, with the observed one, $10^{-120}M_G^4$, by appropriately choosing $M$ and $g$, where $M_G$ is the reduced Planck scale. We also demand that the tunneling rate from $|n=0\rangle$, $\Gamma\approx Ke^{-\frac{16\pi^2}{g^2}}$, is small enough to guarantee that there is no transition within the current Hubble volume, $H_0^{-3}$, in the cosmic age, $\Gamma H^{-4}_0 \mbox{\raisebox{-1.0ex}{$\stackrel{\textstyle <} {\textstyle \sim}$ }}1$. Then we obtain FORMULA where $\alpha\equiv g^2/(4\pi)$ is the coupling strength at the energy scale $M/\sqrt{2}$. If the above inequality is marginally satisfied, we find $\alpha=1/44.4$ and $M=5\times 10^{16}$GeV, which is much larger than the upper bound on both the amplitude of quantum fluctuation, $H/(2\pi)$, during inflation [CIT] and the reheat temperature after inflation [CIT]. If, on the other hand, we take $M=M_G$ so that the cutoff scale of instanton is identical to the presumed field-theory cutoff, we find $\alpha=1/47.$ | 1,039 | hep-ph/0210245 | 2,858,289 | 2,002 | 10 | 17 | false | true | 1 | UNITS |
The Standard Model in particle physics is described by a relativistic quantum field theory and is experimentally verified below the energy scale of $10^{3} GeV$. On the other hand, the Planck energy scale, where quantum gravitational force becomes important, is at $10^{19} GeV$. Therefore, we need to extrapolate $16$ orders of magnitude to guess the new physics beyond the standard framework of relativistic quantum field theory. It is quite conceivable that Einstein's principle of relativity is not valid at Planck's energy scale, it could emerge at energies much lower compared to the Planck's energy scale through the magic of renormalization group flow. This situation is analogous to one in condensed matter physics, which deals with phenomena at much lower absolute energy scales. The "basic\" laws of condensed matter physics are well-known at the Coulomb energy scale of $1\sim 10 eV$; almost all condensed matter systems can be well described by a non-relativistic Hamiltonian of the electrons and the nuclei [CIT]. However, this model Hamiltonian is rather inadequate to describe the various emergent phenomena, like superconductivity, superfluidity, the quantum Hall effect (QHE) and magnetism, which all occur at much lower energy scales, typically of the order of $1 meV$. These systems are best described by "effective quantum field theories\", not of the original electrons, but of the quasi-particles and collective excitations. In this lecture, I shall give many examples where these "effective quantum field theories\" are relativistic quantum field theories or topological quantum field theories, bearing great resemblance to the Standard Model of elementary particles. The collective behavior of many strongly interacting degrees of freedom is responsible for these striking emergent phenomena. The laws governing the quasi-particles and the collective excitations are very different from the laws governing the original electrons and nuclei [CIT]. This observation inspires us to construct models of elementary particles by conceptually visualizing them as quasi-particles or collective excitations of a quantum many-body system, whose basic constituents are governed by a simple non-relativistic Hamiltonian. This point of view is best summarized by the following diagram: | 2,297 | hep-th/0210162 | 2,858,833 | 2,002 | 10 | 17 | false | true | 3 | UNITS, UNITS, UNITS |
Consider gyroresonance scattering in the presence of collisionless damping. The cutoff of fast modes corresponds to the scale where $\tau _{fk}\gamma _{d}\simeq 1$ and this defines the cutoff scale $k_{c}^{-1}$. Using the tensors given in Eq. (REF) we obtain the corresponding Fokker-Planck coefficients for the CRs interacting with fast modes by integrating Eq.(REF) from $k_{min}$ to $k_{c}$ (see Fig.(REFb)). When $k_{c}^{-1}$ is less than $r_{L}$, the results of integration for damped and undamped turbulence coincides. Since the damping increases with $\beta$, the scattering frequency decreases with $\beta$. | 615 | astro-ph/0211031 | 2,880,003 | 2,002 | 11 | 2 | true | false | 1 | FOKKER |
We can relate $H_R$ to the reheating temperature and the Planck mass $G^{-\frac12}$ through the equation FORMULA and the Einstein-Friedman equation FORMULA where $g^*$ is the effective number of degrees of freedom at the reheating temperature and we introduced the scale $M_*$ of the order of the Planck mass FORMULA In radiation dominated epoch the time-dependence of the mass term (REF) is given by the expression FORMULA where we see the emergence of a new mass scale FORMULA This scale will play an important role in the following discussion and in the comparison with results obtained in Minkowski space-time [CIT]. There is a last scale which plays a relevant role, the horizon scale $r_H(\eta)$ which is fixed by the evolution on the time of the Hubble constant: FORMULA Modes with physical wavelength $\lambda_{phys}=\frac{2\pi}{k_{phys}}$ inside the horizon FORMULA are causally connected, modes outside the horizon are causally disconnected. | 951 | hep-ph/0211022 | 2,880,123 | 2,002 | 11 | 2 | true | true | 2 | UNITS, UNITS |
where the time scales $P \approx 10^{3}$ Gyr $\gg Q \approx 40-50$ Gyr are considerably greater than the Hubble time scale of 10-15 Gyr of standard cosmology. The function $\tau(t)$ is very nearly like $t$, with significantly different behaviour for short duration near the minima of the function $S(t)$. The parameter $\eta$ has modulus less than unity thus preventing the scale factor from reaching zero. Typically, $\eta \sim 0.8-0.9$. Hence there is no spacetime singularity, nor a violation of the law of conservation of matter and energy, as happens at the big bang epoch in the standard model. This is because, matter in the universe is created through minibangs, through explosive processes in the nuclei of existing galaxies that produce matter and an equal quantity of a negative energy scalar field $C$. Such processes take place whenever the energy of the $C$-field quantum rises above the threshold energy $m_{\rm P} c^2$, the restmass energy of the Planck particle which is typically created. For details of the basic physics see Hoyle et al (1995) and for models of the kind (1) see Sachs et al (1997). | 1,117 | astro-ph/0211036 | 2,880,755 | 2,002 | 11 | 4 | true | true | 1 | MPS |
- The magnitude of the residual cosmological term is again of the general form ${\frac12} (v/F_v)^2 e^{{-8\pi^2}/{g_v^2}} \Lambda_v^4$ for $v/F_v \ll 1$, then saturating, but now with $g_v$ and $\Lambda_v$ no longer tied to QCD. This could fit the observed value, for example, with $v/F_v \sim 1$, $\Lambda_v \sim M_{\rm Planck}$, and $\alpha_v \sim 0.01$. | 356 | hep-ph/0212128 | 2,937,404 | 2,002 | 12 | 9 | false | true | 1 | UNITS |
It should be clear that solution (REF) represents an equivalent M-theory background for (D6,D8) solution with $B$-field. It is rather appropriate to discuss decoupling limits of this solution when string coupling becomes large. Corresponding scaling limits for (REF) when $\alpha'\to0$ can be determined and these are FORMULA with $\tilde a_x$ and $\tilde a_y$ are fixed area parameters. Note that the areas of transverse $T^2$s also shrink to zero under this scaling. It can be checked that the background (REF) indeed gets decoupled in the limit (REF). So in the IR region where the size of eleventh dimension measured in Planck units $R_{11}(u)/l_p =e^{2\phi/3}$ becomes large it is useful to study above decoupling limits where $l_p\to 0$. The corresponding boundary field theory would be a non-local $6D$ (0,2) SCFT on a circle [CIT]. The nonlocality arises due to the presence of Taub-NUT charges in the M5-brane solutions.[^10] Let us note down the curvature of the 11-dimensional spacetime measured in the Planck units in the IR region (using eq. (REF)) FORMULA The eleven-dimensional curvature measured in Planck units is still large when $u\to0$. Therefore this low energy supergravity description will not be reliable as corresponding (M5,KK) backgrounds would receive higher curvature corrections. But as we saw NCYM and the CFT theories in this region are weakly coupled and can make a good description. | 1,416 | hep-th/0212103 | 2,939,783 | 2,002 | 12 | 10 | false | true | 3 | UNITS, UNITS, UNITS |
Another aspect of the standard theory fares less well in the case of MBH binaries. We have so far discussed the time-independent Fokker-Planck equation; strictly speaking, however, time-independent solutions do not exist as stars that diffuse into the loss cone are moved from one orbit to another, or removed from the system. The flux of stars into the loss cone given by the standard theory is shown in Figure REFb. As the stellar orbital integrals diffuse, the potential changes accordingly, and the isotropic distribution $\bar f(E)$ adjusts to the changing potential. [CIT] :01 demonstrated that the change of the overall density profile of the galaxy can amount to a destruction of the steep central cusp. One may attempt to account for the changing galaxy profile by adjusting $\bar f(E)$ as dictated by the isotropic Jeans equation, while keeping the formal solution in equation (REF) unchanged. Similarly, as the MBH binary hardens, the loss cone boundary $R_{\rm lc}$ decreases. One could try scaling the formal solution to accommodate a changing $R_{\rm lc}$. | 1,070 | astro-ph/0212459 | 2,957,574 | 2,002 | 12 | 20 | true | false | 1 | FOKKER |
The discussion so far has been purely classical. The introduction of quantum theory adds a new dimension to this problem. Much of the early work [CIT] as well as the definitive work by Pauli [CIT] involved evaluating the sum of the zero point energies of a quantum field (with some cut-off) in order to estimate the vacuum contribution to the cosmological constant. Such an argument, however, is hopelessly naive (inspite of the fact that it is often repeated even today). In fact, Pauli himself was aware of the fact that one must *exclude* the zero point contribution from such a calculation. The first paper to stress this clearly and carry out a *second order* calculation was probably the one by Zeldovich [CIT] though the connection between vacuum energy density and cosmological constant had been noted earlier by Gliner [CIT] and even by Lemaitre [CIT]. Zeldovich assumed that the lowest order zero point energy should be subtracted out in quantum field theory and went on to compute the gravitational force between particles in the vacuum fluctuations. If $E$ is an energy scale of a virtual process corresponding to a length scale $l=\hbar c/E$, then $l^{-3}=(E/\hbar c)^3$ particles per unit volume of energy $E$ will lead to the gravitational self energy density of the order of FORMULA This will correspond to $\Lambda L_P^2\approx (E/E_P)^6$ where $E_P=(\hbar c^5/G)^{1/2}\approx 10^{19}$GeV is the Planck energy. Zeldovich took $E\approx 1$ GeV (without any clear reason) and obtained a $\rho_\Lambda$ which contradicted the observational bound "only" by nine orders of magnitude. | 1,595 | hep-th/0212290 | 2,962,647 | 2,002 | 12 | 23 | true | true | 1 | UNITS |
In the Standard Model, running coupling constants for $SU(2)$ and $SU(3)$ at Planck scale deviate by approximately 3 from the critical values for $SMG$ lattice theory (i.e. from the low energy values of the coupling constants extrapolated to the Planck scale). This can be explained if we assume that there are three generations, and the Standard Model group $SMG$ comes about at Planck scale, by the breakdown of $(SMG)^3$ to the diagonal subgroup. With $N_{gen}=3$, FORMULA and the special case where $g_1=g_2=g_3$ corresponds to the diagonal subgroup, FORMULA The $1/g^2$ for the diagonal subgroup couplings being approximately three times larger than for the single $SU(2)$ and $SU(3)$ subgroups, suggests that these inverses of the squared coupling are exactly three times larger for the non-abelian subgroups. This constitutes a prediction of three generations. | 867 | hep-ph/0301029 | 2,973,220 | 2,003 | 1 | 6 | false | true | 3 | UNITS, UNITS, UNITS |
It has been shown by Lancellotti & Kiessling (2001) that the Fokker-Planck equation admits a unique scale invariance, and that therefore the self-similar solution requires a limiting density profile $\rho \propto r^{-3},$ i.e. $\alpha =3.$ Here it is shown why the value of $\alpha$ is not determined by the scale invariance of the Fokker-Planck equation. | 356 | astro-ph/0301166 | 2,978,355 | 2,003 | 1 | 10 | true | false | 2 | FOKKER, FOKKER |
The predicted flux from the ring, $F_{ring}$ is: FORMULA where $D_{*}$ is the distance to the star from the Sun, $R_{in}$ and $R_{out}$ represent the inner and outer radii of the dust ring, $i$ is the inclination angle of the ring and $B_{\nu}$ is the Planck function. With the substitution that $x$ = $h{\nu}/kT_{ring}$, then: FORMULA | 336 | astro-ph/0301411 | 2,993,438 | 2,003 | 1 | 21 | true | false | 1 | LAW |
The presentation is organized as it follows. In Section II, to make the presentation self contained and to fix the notation, a brief outline on the Galilei covariance is presented. The Fokker-Planck equation is derived from an-abelian gauge invariant Lagrangian in Section III, and in Section IV the non-abelian situation is addressed. Final concluding and remarks are presented in Section V. | 392 | hep-ph/0301197 | 2,996,771 | 2,003 | 1 | 22 | false | true | 1 | FOKKER |
Rather remarkably, one finds that without using any observational data except for certain discrete integers (e.g., the dimension of space, the number of generations of quarks and leptons, etc.), one can get crude estimates for typical observed values of both of these parameters that are in the right ballpark to explain our particular observations. In this paper I shall show how one can get a crude estimate for the magnitude of the charge of the proton ($e \equiv \sqrt{\alpha}$ in Planck units) that differs from what we observe by only a few percent. One can also get a somewhat more crude estimate for the mass of the proton ($m_p \equiv \sqrt{\alpha_G}$ in Planck units) that differs by about 3 orders of magnitude from the value that we observe. However, since the observed value is about 19 orders of magnitude smaller than unity, on a logarithmic scale the crude estimate is not that far off. | 902 | hep-th/0302051 | 3,019,722 | 2,003 | 2 | 7 | true | true | 2 | UNITS, UNITS |
A discrete R-symmetry $Z_{NR}$ often appears as a remnant of the rotational symmetry of the compactified extra space in higher dimensional supergravity or string theory [CIT]. This discrete R-symmetry should be nonanomalous since this is a gauge symmetry. An R-symmetry plays a crucial role in the phenomenology of supersymmetric (SUSY) theory. First, it can suppress the cosmological constant compared to the Planck scale. Second, the SUSY-invariant mass term (the $\mu$-term) of the Higgs chiral multiplet can be forbidden so that the Higgs mass not be the Planck scale. If an R-symmetry breaking is related to SUSY breaking, the Higgs chiral multiplet can obtain a mass of the order of the gravitino mass $m_{3/2} \simeq 1 \mbox{TeV}$ by the Giudice-Masiero (GM) mechanism [CIT]. Third, an R-parity forbids the dimension-four baryon and lepton number violating operators causing too rapid proton decay [CIT]. These observations motivate us to ask whether we can find a nonanomalous discrete R-symmetry with the above properties. In a paper by Kurosawa, Maru and Yanagida [CIT], nonanomalous discrete R-symmetries in the minimal SUSY standard model (MSSM) and the SUSY grand unified theory (GUT) were found under the situation that the GM mechanism works. These solutions can also forbid the dimension-five baryon- and lepton-number violating operators. Furthermore, extra fields ${\bf 5} \oplus {\bf 5^*}$ with the mass of order $1 \mbox{TeV}$, which can be testable in collider experiments, are predicted from the anomaly cancellations in the GUT case. | 1,556 | hep-ph/0302163 | 3,033,134 | 2,003 | 2 | 18 | false | true | 2 | UNITS, UNITS |
Supersymmetric grand unified theories (GUTs) provide an especially attractive framework for physics beyond the standard model (and MSSM), and it is therefore natural to ask if there exists in this framework a compelling, perhaps even an intimate connection with inflation. In ref. [CIT] one possible approach to this question was presented. In its simplest realization, inflation is associated with the breaking at scale $M$ of a grand unified gauge group $G$ to $H$. Indeed, inflation is 'driven' by quantum corrections which arise from the breaking of supersymmetry by the vacuum energy density in the early universe. The density fluctuations, it turns out, are proportional to $(M/M_{\rm Planck})^2$, where $M_{\rm Planck}\simeq 1.2\times 10^{19}$ GeV denotes the Planck mass. From the variety of $\delta T/T$ measurements, especially by the Wilkinson Microwave Anisotropy Probe (WMAP) [CIT], the symmetry breaking scale $M$ is of order $10^{16}$ GeV, essentially identical to the scale of supersymmetric grand unification. | 1,026 | astro-ph/0302504 | 3,041,649 | 2,003 | 2 | 25 | true | true | 3 | UNITS, UNITS, UNITS |
There have been proposals that primordial black hole remnants (BHRs) are the dark matter, but the idea is somewhat vague. We argue here first that the generalized uncertainty principle (GUP) may prevent black holes from evaporating completely, in a similar way that the standard uncertainty principle prevents the hydrogen atom from collapsing. Secondly we note that the hybrid inflation model provides a plausible mechanism for production of large numbers of small black holes. Combining these we suggest that the dark matter might be composed of Planck-size BHRs and discuss the possible constraints and signatures associated with this notion. | 645 | astro-ph/0303349 | 3,071,477 | 2,003 | 3 | 15 | true | false | 1 | MISSION |
The *Kähler potential* for the fields is the so called no-scale potential. It takes the following canonical form: FORMULA In (REF) and elsewhere we have set the Planck scale $M_P^{(4d)}$ to unity, i.e., all dimensional quantities are scaled by appropriate powers of $M_P^{(4d)}$. | 279 | hep-th/0303208 | 3,083,677 | 2,003 | 3 | 24 | false | true | 1 | UNITS |
The Minimal Supersymmetric Standard Model (MSSM) contains a scale $\mu$, the Higgs-higgsino mass parameter in the superpotential, which is phenomenologically constrained to lie not far from the electroweak scale [CIT]; in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) this mass parameter may be linked dynamically to the electroweak scale in a natural way [CIT] -- [CIT]. The superpotential of the MSSM must be analytic in the fields, preventing the use of only one Higgs doublet for the generation of both up-type and down-type quark masses. Thus the model requires two Higgs doublets, which is also necessary to maintain an anomaly free theory. One of the doublets ($H_u$) provides a mass for up-type quarks while the other ($H_d$) provides a mass for down-type quarks and charged leptons. The term $\mu H_u H_d$ in the superpotential of the MSSM mixes the two Higgs doublets. Since the parameter $\mu$, present before the symmetry is broken, has the dimension of mass, one would naturally expect it to be either zero or the Planck scale ($M_{\rm Pl}$). However, if $\mu=0$ then the form of the renormalization group equations [CIT] implies that the mixing between Higgs doublets is not generated at any scale; the minimum of the Higgs potential occurs for $\langle H_d \rangle=0$, causing the down-type quarks and charged leptons to remain massless after symmetry breaking. In the opposite case, for $\mu\simeq M_{\rm Pl}$, the Higgs scalars acquire a huge contribution $\mu^2$ to their squared masses and the fine tuning problem is reintroduced. Indeed, one finds that $\mu$ is required to be of the order of the electroweak scale in order to provide the correct pattern of electroweak symmetry breaking. | 1,720 | hep-ph/0304049 | 3,098,998 | 2,003 | 4 | 4 | false | true | 1 | UNITS |
The AQD as a detector is suitable to measure the de Sitter time interval, because it couples linearly to the square root of the density of the superfluid gas. In principle, one can construct detectors coupling to different powers of density or superfluid velocity, and then more generally experimentally study the non-uniqueness of the particle content of various quantum states in curved space-time [CIT]. For example, outcoupling pairs of atoms by photoassociation is a means to set up a detector which has $d\tau/dt \propto \rho_0$. Finally, we note that while in this paper we have studied only the $n=0$ massless axial phonon modes, strongly elongated condensates can also be used to study the evolution of massive bosonic excitations. Together with a natural Planck scale $E_{\rm Planck} \sim \mu$, this provides the opportunity to investigate, on a laboratory scale, the influence of finite quasiparticle mass and the trans-Planckian spectrum on the propagation of relativistic quantum fields in curved space-time. | 1,021 | cond-mat/0304342 | 3,112,676 | 2,003 | 4 | 15 | false | true | 2 | UNITS, UNITS |
Let us consider the mass-like quantum conformal Minkowskian algebra introduced in [CIT], $U_\tau(so(4,2))$, where $\tau$ is the deformation parameter. The ten Poincaré generators together with the dilation close a Weyl--Poincaré (or similitude) Hopf subalgebra, $U_\tau({\cal WP})\subset U_\tau(so(4,2))$. Such a deformation is the natural extension to 3+1 dimensions of the results previously presented in [CIT] for the time-type quantum $so(2,2)$ algebra and, in fact, is based in the Jordanian twist (introduced in [CIT]) that underlies the non-standard (or $h$-deformation) $U_\tau(sl(2,{\mathbb R}))$ [CIT]. Thus $U_\tau(so(4,2))$ verifies the following sequence of Hopf subalgebra embeddings: FORMULA This, in turn, ensures that properties associated to deformations in low dimensions are fulfilled, by construction, in higher dimensions and moreover any physical consequence derived from the structure of $U_\tau({\cal WP})$ is consistent with a full quantum conformal symmetry that can further be developed. Therefore, throughout the paper we will restrict ourselves to analyse the DSR theory provided by the deformed Weyl--Poincaré symmetries after the identification of the deformation parameter with the Planck length: $\tau\sim L_p$. | 1,245 | hep-th/0305033 | 3,140,157 | 2,003 | 5 | 5 | false | true | 1 | UNITS |
FORMULA where the $\left\{ j_{i}\right\}$ have integers and half-integers values, $l_{p}=(\hbar G/c)^{1/2}=10^{-33} \hbox{cm}$ is the Planck length and $\gamma$ is a constant analogous to the Immirzi parameter [CIT]. The spectrum of the area operator is a very important result of loop quantum gravity. However, considering the recent numerical analysis of spin foam models [CIT], it is possible that the correct area formula is given not by equation (REF) but by FORMULA This result was proposed in Ref. [CIT] and our analysis for a two dimensional non-commutative space agrees with this spectra. | 598 | hep-th/0305080 | 3,147,415 | 2,003 | 5 | 9 | false | true | 1 | UNITS |
\(i\) In all static space-times with horizons, it can be shown that this boundary term is proportional to the area of the horizon. As the surface approaches the one-way horizon from outside, the quantity $N(a_in^i)$ tends to $(-\kappa)$, where $\kappa$ is the surface gravity of the horizon and is constant over the horizon [CIT]. Using $\beta\kappa=2\pi$, the contribution of the horizon becomes FORMULA Our result therefore implies that the area of the horizon, as measured by *any* observer blocked by that horizon, will be quantized. (In normal units, $A_{\rm boundary}=2\pi m\hbar$ and $A_{\rm horizon}=8\pi m(G\hbar/c^3)=8\pi mL_{\rm Planck}^2$). In particular, any flat spatial surface in Minkowski space-time can be made a horizon for a suitable Rindler observer, and hence all area elements in even flat space-time must be intrinsically quantized. In the quantum theory, the area operator for one observer need not commute with the area operator of another observer, and there is no inconsistency in all observers measuring quantized areas. The changes in area, as measured by any observer, are also quantized, and the minimum detectable change is of the order of $L_{\rm Planck}^2$. It can be shown, from very general considerations, that there is an operational limitation in measuring areas smaller than $L_{\rm Planck}^2$, when the principles of quantum theory and gravity are combined [CIT]; our result is consistent with this general analysis. | 1,458 | hep-th/0305165 | 3,161,126 | 2,003 | 5 | 19 | true | true | 3 | UNITS, UNITS, UNITS |
It is worth observing that even though the total divergence form of $A_{\rm boundary}$ and its quantization (REF) would hold in the complete quantum theory of gravity, the interpretation of $A_{\rm boundary}$ in terms of the horizon area holds only in the lowest order effective theory, and in the semiclassical limit. Higher order corrections can change the form of $A_{\rm boundary}$ so that it no longer is proportional to the horizon area, while the true quantum area operator can differ from the $A_{\rm boundary}$ term which only measures the projection of the area operator on the horizon surface. Staying within the lowest order effective theory means that one should not go very close to the horizon, and semiclassical limit means that the horizon area parameter $m$ should be large enough. With the usual power counting counting arguments, these conditions can be quantified to mean that our result for $A_{\rm boundary}$ is valid up to ${\cal O}(L^{-1}_{\rm Planck})$ and ${\cal O}(\ln m)$ corrections. | 1,013 | hep-th/0305165 | 3,161,140 | 2,003 | 5 | 19 | true | true | 1 | UNITS |
- In several new physics models, a new scale, usually called the intermediate scale, $M_{\rm Int}\sim \sqrt{m_W M_{\rm Pl}}\sim 10^{11} {\rm GeV}$, is introduced. For example, supersymmetry breaking has to occur at this scale if it is mediated via Planck scale physics to the observable sector. The values obtained assuming $m_D \sim m_\tau$ in both eqs. (REF) and (REF) are very close to $M_{\rm Int}$. This could be an indication that neutrino masses are also generated by such models. | 487 | hep-ph/0305245 | 3,167,130 | 2,003 | 5 | 22 | false | true | 1 | UNITS |
Of course, the estimates we are providing in this section are crude and idealized. It is somewhat encouraging that at least at this level the suppression induced by the smallness of the Planck length does not appear to be unsurmountable, since, even at the same crude level of analysis, most other experimental setups would immediately prove to be inadequate for Planck-scale studies). In the next Section we discuss some interferometric setups that could be used to find evidence of the Planck-scale effects we are considering. This will provide the basis for our more realistic discussion, in Section 4, of the challenges that must be faced in order to render meaningful the encouraging naive estimate we obtained here. | 721 | gr-qc/0306019 | 3,183,586 | 2,003 | 6 | 4 | true | true | 3 | UNITS, UNITS, UNITS |
Since $\lambda$ must be taken very small, on the order of $10^{-12}$, for the density perturbations to have the right magnitude, this value for the field is generally well above the Planck scale. The corresponding energy density, however, is given by FORMULA which is actually far below the Planck scale. | 304 | astro-ph/0306275 | 3,197,589 | 2,003 | 6 | 13 | true | false | 2 | UNITS, UNITS |
Yet another argument leading to the same conclusion comes from the existence of the Kodama state [CIT], which is an exact physical quantum state of the gravitational field for nonzero $\Lambda$, which has a semiclassical interpretation in terms of deSitter. One can argue that a large class of gauge and diffeomophism invariant perturbations of the Kodama state are labeled by quantum spin networks of the algebra $SU_q(2)$ with again (REF) [CIT]. However, of those, there should be a subset which describe gravitons with wavelengths $\sqrt{\Lambda} > k > E_{Planck}$, moving on the deSitter background as such states are known to exist in a semiclassical expansion around the Kodama state [CIT]. One way to construct such states is to construct quantum spin network states for $SO_q(3,2)$, and decompose them into sums of quantum spin network states for $SU_q(2)$. The different states will then be labeled by functions on the coset $SO_q(3,2)/SU_q(2)$. | 955 | hep-th/0306134 | 3,201,732 | 2,003 | 6 | 16 | false | true | 1 | UNITS |
In the previous Section we have shown that the Planck-scale effects considered here would affect the production of charged pions before the ultra-high-energy cosmic-ray proton escapes the source. In this Section we analyze the implications of the same effects for the decay processes $\pi^+ \rightarrow \mu^+ + \nu_\mu$ and $\mu^+ \rightarrow e^+ + \nu_e + {\bar{\nu}}_\mu$ which are also relevant for the Bahcall-Waxman bound. | 427 | hep-ph/0307027 | 3,228,763 | 2,003 | 7 | 2 | true | true | 1 | UNITS |
However, in the special scale relativity framework, these questions are set in a fundamentally different way. Indeed, the laws of dilation have a log-lorentzian form (as a direct manifestation of the principle of scale relativity), so that a new relation between length-time-scales and energy-momentum scales is established [CIT], that reads (when taking as reference the Z boson scale): FORMULA A major consequence of this new structure of space-time is that the Planck length-time scale becomes invariant under dilations and now plays the role devoted to the zero point. The Planck mass scale is no longer its inverse. From Eq. (REF) one finds that it corresponds in the new framework to a length-scale $\lambda_G$ given by $\ln(\lambda_Z/\lambda_G)=\ln(m_{I \!\!\!\! P}/m_Z) / \sqrt{2}$, which is nothing but the unification scale [CIT]. | 840 | hep-th/0307093 | 3,243,114 | 2,003 | 7 | 10 | false | true | 2 | UNITS, UNITS |
E.D.Jones [CIT] has sketched a compelling cosmological scenario resting on basic physical principles. Starting from the fact that the validity of current physics is bounded, at best, by the Planck length and the Planck density, he assumes only scaling laws are needed to take the universe from some pre-geometric, pre-physical situation by an "extremely rapid\" transition to a much less dense phase in which space, time, particles and temperature carry their usual meaning. He and we refer to the end of this transition as *thermalization*. The only parameter which is unknown is the "number of Plancktons\" --- a *Planckton* is a Planck's mass worth of mass-energy at the Planck density and temperature --- with which, in a poetic sense, our universe "starts out\". An initial presentation of Jones' ideas by Noyes, et. al. is available [CIT], with the *caveat* that Jones' own views could differ in ways that have not yet been spelled out. What makes Jones' work so exciting is that with this minimal input he is able to show that a currently acceptable value of $\Omega_{\Lambda}= 0.7$ for the cosmological constant density normalized to the critical density implies that the mass scale at which thermalization becomes meaningful is about 5 Tev. In this paper we present a calculation leading to this result and discuss some of the implications. | 1,349 | hep-th/0307250 | 3,261,801 | 2,003 | 7 | 24 | false | true | 4 | UNITS, UNITS, UNITS, UNITS |
This type of analysis could eliminate the requirement in the MASTER method for the calibration of power spectrum transfer functions via simulations (see equation 15 of Hivon *et al.* 2002). In addition, the covariance matrix of the hybrid estimator would reflect the effects of correlated noise at low multipoles accurately, since it uses the QML Fisher matrix as an input. However, in this approach, the effects of $1/f$ noise would not be properly included in the PCL estimates. Fortunately, for the parameters of the Planck instruments, the effects of $1/f$ noise should be confined to low multipoles ($\ell \lower.5ex\hbox{$\; \buildrel < \over \sim \;$}100$, see *e.g.* Keihänen *et al.* 2003) and the pixel-pixel noise should be strongly diagonally dominated (*e.g.* Stompor and White 2003) suggesting that PCL estimates and the analytic estimates of their covariance matrix should be accurate. The effects of realistic $1/f$ noise on the hybrid estimator clearly need to tested against numerical simulations. | 1,015 | astro-ph/0307515 | 3,268,869 | 2,003 | 7 | 30 | true | false | 1 | MISSION |
Such a remnant can be applicable to explain the dark matter of the universe [CIT]. The scenario is as follows. Primordial black holes are created by the density-fluctuation in the very early universe and are later made to dominate over the universe by the universe expansion. The Hawking radiation of the black hole reheats up the universe and the spherical EW wall thermally formed around the black hole provides the baryon number for the universe. The black hole obtains some charge by our charge-up process and becomes the Planck-massive remnant as the main constituent of the dark matter. Finally we expect that the formation of the spherical wall around the black hole plays crucial roles in the cosmology. | 711 | hep-th/0307294 | 3,270,556 | 2,003 | 7 | 30 | false | true | 1 | UNITS |
In the following we address the issue of how much of an actual improvement over the two step method can be expected from such an approach in a case of a realistic planck-like experiment. Given that, on the ring level, the two-stage method exploits only the pixel domain constraints, while the full optimal map-making attempts to make use of both pixel and time domain ones, this question is clearly just a rephrasing of the problem posed in the previous Section. At the computational level we can turn this problem into a question of how the time domain derived constraints on the relative offsets of two rings compare with those derived from the pixel domain. Alternately, as uncertainty in the recovery of the rings offsets results in the presence of strongly correlated linear features in the map aligned with the scan direction (i.e., *stripes*), we will refer to that problem as striping. | 893 | astro-ph/0308186 | 3,285,393 | 2,003 | 8 | 11 | true | false | 1 | MISSION |
We show that the Faddeev-Popov distribution, $P_{\rm FP}$ given by (REF), is a stationary solution of the gauge fixed Fokker-Planck equation FORMULA which is derived from the stochastic-time evolution equation of the expectation value of observables in (REF) under the appropriate choice of the gauge fixing functions $\phi$ and ${\bar \phi}$. Namely, the r.h.s. of the Fokker-Planck equation (REF) vanishes for $P_{\rm FP}$, provided that the gauge fixing functions are defined by FORMULA | 490 | hep-th/0308081 | 3,289,824 | 2,003 | 8 | 13 | false | true | 2 | FOKKER, FOKKER |
In our derivation of the D-brane tension in three dimensions, we shall first describe how the appropriate factors of the string coupling constant $g_s$ appear. For this, we need to describe how to incorporate the string dilaton field into the topological membrane formalism. This problem was addressed in [CIT] and consists of examining the conformal coupling of topologically massive gauge theory to topologically massive gravity through the action FORMULA which is defined on a three-manifold $M$. Here $\kappa$ is the three-dimensional Planck mass, $R(\omega)$ is the curvature of the torsion-free, $SO(2,1)$ Lie algebra valued spin-connection $\omega_\mu^a$ of the frame bundle of $M$, and $D$ is a dimensionless scalar field in three spacetime dimensions. The first term in (REF) is a modification of the Einstein-Hilbert action, while FORMULA is the sum of the gauge and gravitational Chern-Simons actions. | 912 | hep-th/0308101 | 3,292,086 | 2,003 | 8 | 15 | false | true | 1 | UNITS |
Recent measurements of atmospheric and solar neutrino fluxes at the Super Kamiokande [CIT] and the Sudbury Neutrino Observatory [CIT] have provided compelling evidence for neutrino masses and neutrino oscillations. This received further support from the reactor KamLand experiment [CIT]. Furthermore, the Wilkinson Microwave Anisotropy Probe [CIT] imposes the constraint that the sum of neutrino masses to be less than $.75$ eV. Such a small value for neutrino masses is generally considered to be a harbinger of new physics beyond the standard model (SM) and the existence of a new scale between the Fermi and the Planck scale. In particular if the three neutrinos involved in weak interactions are Majorana in nature then clearly new physics is at play. The most popular suggestion of generating neutrino masses in the milli-electronvolt range is grand unified theories (GUTs) via the seesaw mechanism with or without supersymmetry. Central to this idea is the introduction of one right-handed singlet neutrino per family of the SM fermions with a mass near the GUT scale. This is natural in $SO(10)$ models since its fundamental $\mathbf {16}$ representation encompasses this singlet with the 15 fermions of the SM. For a recent review of neutrino masses in grand unified models see [CIT]. On the other hand small Dirac neutrino masses is considered unnatural due to the extreme fine tuning required. However, in theories with extra dimensions this can be generated by allowing the singlet neutrinos to be bulk fields. A small Yukawa coupling can be obtained due to the volume dilution factor if the extra dimensions are sufficiently large [CIT]. In both cases right-handed singlet fields $N_R$ are necessary. | 1,712 | hep-ph/0308187 | 3,295,158 | 2,003 | 8 | 19 | false | true | 1 | UNITS |
Experiments in atomic systems are very well suited to this approach because they can be sensitive to extremely low energies. Sensitivity to frequency shifts at the level of 1 mHz or less are routinely attained. Expressing this as an energy shift in GeV corresponds to a sensitivity of roughly $4 \times 10^{-27}$ GeV. This sensitivity is well within the range of energy one would associate with suppression factors originating from the Planck scale. For example, the ratio $m_e/M_{\rm Pl}$ multiplying the electron mass yields an energy of approximately $2.5 \times 10^{-26}$ GeV. | 580 | hep-ph/0308281 | 3,305,270 | 2,003 | 8 | 27 | false | true | 1 | UNITS |
Quantum physics and gravity are believed to combine at the Planck scale, $m_P \simeq 10^{19}$ GeV. Experimentation at this high energy is impractical, but existing technology could detect suppressed effects from the Planck scale, such as violations of relativity through Lorentz or CPT breaking [CIT]. At experimentally accessible energies, signals for Lorentz and CPT violation are described by the Standard-Model Extension (SME) [CIT], an effective quantum field theory based on the Standard Model of particle physics. The SME incorporates general coordinate-independent Lorentz violation. | 591 | hep-ph/0308300 | 3,307,183 | 2,003 | 8 | 28 | false | true | 2 | UNITS, UNITS |
The temperature correction to the free energy of the gravitational field is considered which does not depend on the Planck energy physics. The leading correction may be interpreted in terms of the temperature dependent effective gravitational constant G_{eff}. The temperature correction to G_{eff}^{-1} appears to be valid for all temperatures T<< E_{Planck}. It is universal since it is determined only by the number of fermionic and bosonic fields with masses m<< T, does not contain the Planck energy scale E_{Planck} which determines the gravitational constant at T=0, and does not depend on whether or not the gravitational field obeys the Einstein equations. That is why this universal modification of the free energy for gravitational field can be used to study thermodynamics of quantum systems in condensed matter (such as quantum liquids superfluid 3He and 4He), where the effective gravity emerging for fermionic and/or bosonic quasiparticles in the low-energy corner is quite different from the Einstein gravity. | 1,025 | gr-qc/0309066 | 3,333,026 | 2,003 | 9 | 13 | false | true | 4 | UNITS, UNITS, UNITS, UNITS |
To derive dust masses knowledge of the optical properties of the grains is needed. The grain emissivity can depend quite strongly on grain composition and in particular in the ISOCAM range on wavelength (see e.g. Draine & Lee, [CIT]). Nevertheless, for a first interpretation the dust spectrum may be approximated by a modified blackbody function of the form already used for the colour correction in Sect. [3.1]. The flux density of $N(a)$ dust grains with radius $a$ at a distance $D$ radiating at a certain temperature $T$ is then given by FORMULA where the emission coefficient is assumed to be $Q_\lambda(a)=a,\xi,\lambda^{-\beta}$ with constant factors $\xi$ and $\beta$. The total luminosity of such a spectrum is given by: FORMULA where $k$, $h$, $c$ and $\sigma$ are the Boltzmann constant, the Planck constant, the velocity of light and the Stefan--Boltzmann constant. $\left<Q(T,a)\right>$ is the Planck--averaged emission coefficient and $\Gamma(x)$ and $\zeta(x)$ are the gamma- and the zeta-functions. Whereas the emission behaviour of spherical small grains at long wavelengths can be described with $\beta=2$ at shorter wavelengths a better approximation is given by $\beta=1$. The fit of a spectrum with $\beta=1$ including a colour correction to the flux densities measured with ISOCAM is shown in Fig. REF. The corresponding temperature is $236.0\pm 11.5$ K and the luminosity of the best fit is $L=2.47\times 10^{28} {\rm W}$. As seen in the figure the approximation gives a good explanation of the observed colours ($\chi^2=0.14$). | 1,552 | astro-ph/0309475 | 3,338,594 | 2,003 | 9 | 17 | true | false | 2 | CONSTANT, CONSTANT |
Having set the stage, it is now instructive to discuss the possible flavour structure of low singlet-scale models with nearly degenerate heavy Majorana neutrinos. Such a class of models may be constructed by assuming that lepton-number violation (and possibly baryon-number violation) occurs at very high energies at the GUT scale $M_{\rm GUT} \sim 10^{16}$--$10^{17}$ GeV, or even higher close to the Planck scale $M_{\rm Planck} \sim 10^{19}$ GeV through gravitational interactions. On the other hand, operators that conserve lepton number are allowed to be at the TeV scale. | 577 | hep-ph/0309342 | 3,358,400 | 2,003 | 9 | 30 | false | true | 2 | UNITS, UNITS |
As illustrated in Fig. REF, high energy protons may interact with cosmic microwave background photons to produce pions. In each interaction of this type, the proton loses a fraction $\sim m_\pi/m_p$ of its energy. The threshold energy requirement, $E_pE_\gamma\gtrsim m_p m_\pi c^4$ where $E_p$ and $E_\gamma$ are the proton and photon energies respectively, implies that protons of energy $E_p>10^{20}$ eV may interact with almost all of the $T=2.7^o$ K background photons, while protons of lower energy may interact only with the tail of the Planck distribution. Thus, the energy loss distance, $\lambda_E(E_p)$, drops rapidly with energy in the range of $0.5\times10^{20}$ eV to $3\times10^{20}$ eV (see Fig. REF). | 717 | astro-ph/0310079 | 3,362,209 | 2,003 | 10 | 2 | true | true | 1 | LAW |
Any candidate theory of quantum gravity must address the breakdown of the classical smooth manifold picture of space-time at distances comparable to the Planck length. String theory, in contrast, is formulated on conventional space-time. However, we show that in the low energy limit, the dynamics of generally curved Dirichlet $p$-branes possess an extended local isometry group, which can be absorbed into the brane geometry as an almost product structure. The induced kinematics encode two invariant scales, namely a minimal length and a maximal speed, without breaking general covariance. Quantum gravity effects on D-branes at low energy are then seen to manifest themselves by the kinematical effects of a maximal acceleration. Experimental and theoretical implications of such new kinematics are easily derived. We comment on consequences for brane world phenomenology.\ *Journal References:* invited article in European Physical Journal C, reprinted in Proceedings of the 41st International School on Subnuclear Physics 2003, Erice, Italy | 1,046 | gr-qc/0310096 | 3,387,938 | 2,003 | 10 | 19 | false | true | 1 | UNITS |
It would be more appropriate to describe inflation as superluminal expansion if all distances down to the Planck length, $l_{\rm pl}\sim 10^{-35}m$, were receding faster than the speed of light. Solving $D_{\rm H}=c/H = l_{\rm pl}$ gives $H = 10^{43}s^{-1}$ (inverse Planck time) which is equivalent to $H= 10^{62}kms^{-1}Mpc^{-1}$. If Hubble's constant during inflation exceeded this value it would justify describing inflation as "superluminal expansion". | 457 | astro-ph/0310808 | 3,400,392 | 2,003 | 10 | 28 | true | false | 2 | UNITS, UNITS |
The same result can also be obtained from what is known as "entanglement entropy" arising from the quantum correlations which exist across the horizon. We saw in Section [4] that if the field configuration inside the horizon is traced over in the vacuum functional of the theory, then one obtains a density matrix $\rho$ for the field configuration outside [and vice versa]. The entropy $S=-Tr(\rho \ln \rho)$ is usually called the entanglement entropy. This is essentially the same as the previous calculation and, of course, $S$ diverges quadratically on the horizon [CIT]. Much of this can be done without actually bringing in gravity anywhere; all that is required is a spherical region inside which the field configurations are traced out [CIT]. Physically, however, it does not seem reasonable to integrate over all modes without any cut off in these calculations. By cutting off the mode at $l \approx L_P$ one can obtain the "correct" result but in the absence of a more fundamental argument for regularising the modes, this result is not of much significance. The cut off can be introduced in a more sophisticated manner by changing the dispersion relation near Planck energy scales but again there are different prescriptions that are available [CIT] and none of them are really convincing. | 1,300 | gr-qc/0311036 | 3,427,249 | 2,003 | 11 | 11 | true | true | 1 | UNITS |
Quantum-gravity effects are extremely small, since their magnitude is typically set by some power of the ratio between the Planck scale and the wavelength of the particle under study. There are some contexts in which the theoretical predictions can be confronted with data, but in most cases it is necessary to rely on observations in astrophysics and cosmology, rather than laboratory experiments [CIT]. The "astrophysics of quantum gravity\" is being considered also for effects that are not directly related to the issues for Lorentz symmetry that I discussed here (see, for example, the Equivalence-Principle tests considered in Refs. [CIT]), and has been advocated in a large number of papers on the fate of Lorentz symmetry in quantum gravity. It is at this point well established that, if Lorentz symmetry is broken or deformed at the Planck scale, there are at least a handful of opportunities for controntation with data. | 930 | astro-ph/0312014 | 3,455,652 | 2,003 | 11 | 30 | true | false | 2 | UNITS, UNITS |
The basic model consists in a Randall-Sundrum type II scenario with a brane-confined inflaton field and no energy exchange between the brane and the bulk. The continuity equation is the standard 4D equation coming from the local conservation of the stress-energy tensor, $\nabla^\nu T_{\mu \nu}=0$: FORMULA and the modified Friedmann equations in this conformally flat background are [CIT] -- [CIT] FORMULA where $H$ is the Hubble parameter restricted to the 3-brane, $\kappa_4^2 \equiv 8\pi/m^2_4$ includes the effective Planck mass $m_4 \simeq 10^{19},{\rm GeV}$, $\lambda$ is the brane tension (constrained to be $\lambda^{1/4}>100,{\rm GeV}$ by gravity experiments) and $\rho$ is the matter density, which is $\rho = \dot{\phi}^2/2 + V =p+2V$ in the case of a homogeneous scalar field with potential $V(\phi)$. The case of brane-bulk energy flow is far richer and will not be treated here (e.g., [CIT] -- [CIT]). In the following, superscripts (*l*) and (*h*) will denote the low- ($\rho\ll \lambda$) and high- ($\rho \gg \lambda$) energy regimes, respectively. | 1,065 | hep-ph/0312246 | 3,486,196 | 2,003 | 12 | 17 | true | true | 1 | UNITS |
Thus, with the current experimental accuracy, we can exclude only models with high $x$ and high $\Omega_{\rm b}'$, but with the soon available high precision data on CMB (Map, Planck) and LSS (2dF and SDSS) we will be able to choose between the CDM and mirror cosmological scenarios. | 283 | astro-ph/0312607 | 3,496,299 | 2,003 | 12 | 23 | true | true | 1 | MISSION |
The most promising candidate that can explain the dynamics of quantum gravity at the Planck scale is string theory. One of the basic results in string theory is the existence of the minimum length scale $l_s$ [CIT], and spacetime is expected to loose its smooth Riemannian structure and to become discrete (or noncommutative) at the Planck scale. At the present moment, however, we do not have an analytic tool in hand with which string dynamics around the Planck scale can be dealt with in a definite manner. In the present paper, we assume that such quantum effects of gravity can be reflected simply by introducing a cutoff or a noncommutative scale $L_{\rm cut},\big(=O(l_s)\big)$ into the dynamics of the inflaton field. We try to understand the large-scale damping by introducing a holographic cutoff to an inflaton field around the Planck scale. | 852 | hep-th/0312298 | 3,499,804 | 2,003 | 12 | 28 | true | true | 4 | UNITS, UNITS, UNITS, UNITS |
Finally, let us consider using a black hole to do computations. This may sound like a ridiculous proposition. But if we believe that black holes evolve according to quantum mechanical laws, it is possible, at least in principle, to program black holes to perform computations that can be read out of the fluctuations in the Hawking black hole radiation. How large is the memory space of a black hole computer, and how fast can it compute? Applying the results for computation derived above, we readily find the number of bits in the memory space of a black hole computer, given by the lifetime of the black hole divided by its resolution time as a clock, to be FORMULA where $m_P = \hbar/(t_P c^2)$ is the Planck mass, $m$ and $r_S^2$ denote the mass and event horizon area of the black hole respectively. This gives the number of bits $I$ as the event horizon area in Planck units, in agreement with the identification of a black hole entropy. Furthermore, the number of operations per unit time for a black hole computer is given by FORMULA its energy divided by Planck's constant, in agreement with the result found by Margolus and Levitin, and by Lloyd [CIT] (for the ultimate limits to computation). It is curious that all the bounds on computation discussed above are saturated by black hole computers. Thus one can even say that once they are programmed to do computations, black holes are the ultimate simple computers. | 1,427 | gr-qc/0401015 | 3,505,679 | 2,004 | 1 | 5 | true | true | 3 | UNITS, UNITS, CONSTANT |
For a photon's field moving along the x-axis, we can at $x = 0$ normalize the Poynting vector, $S$, to the energy flux of one photon, $\hbar \omega_0= h\nu_0$, per second and per square cm in vacuum, where $h$ is the Planck constant. Even in a vacuum, the photon is never infinitely sharp but consists of a distribution of frequency components as indicated by FORMULA where $\gamma$ is the photon width [1]. For the dielectric constant $\varepsilon = (n - i\kappa)^2 = 1$ and therefore the refraction index $n = 1$ and absorption cooefficient, the imaginary part $\kappa = 0 {\rm{,}}$ this form of the field in the photon also follows from Eq.,(3) below, which follows from Eq.,(A29) in the Appendix A. When the photon penetrates a plasma, the photon's virtual field will be modified by the dielectric constant $\varepsilon= (n - i \kappa)^2 {\rm{.}}$ From the solution, Eq.,(A15), to the dynamical Eq.,(A12) of the Appendix A, we get that the polarization is given by Eq.,(A18). From the polarization, we derive that the dielectric constant is given by Eqs.,(A19) and (A20) of the Appendix A. If the binding-energy frequency $\omega_q = 0$ and the collision damping $\alpha = 0{\rm{}}$ (because the collision damping, $\alpha {\rm{,}}$ is included in $\beta \omega^2{\rm{),}}$ we derive from Eq.,(A20) that the dielectric constant is FORMULA where $\omega_p= \sqrt{4\pi e^2N_e/m_e}$ is the plasma frequency, and where $\beta\omega^2$ is the radiation damping in the hot sparse plasma. | 1,485 | astro-ph/0401420 | 3,529,132 | 2,004 | 1 | 21 | true | false | 1 | CONSTANT |
In this section, we analyse the more general case where the bulk gauge couplings of the $SU(2)_L$ and $SU(2)_R$ are different, $g_{5R}$ and $g_{5L}$, and brane kinetic terms allowed by the gauge symmetries of the theory are added. Some of these parameters have already been considered in [CIT], where it was shown that turning on these parameters does not change the leading order predictions for the SM masses and couplings. The AdS/CFT interpretation of different left-right bulk gauge couplings is that the CFT does not have a left-right interchange symmetry, or in other words is a chiral gauge theory, and so in our context such models are analogous to chiral technicolor [CIT]. On the Planck brane, the only allowed kinetic terms involve the locally unbroken SM group SU(2)$_L \times$U(1)$_Y$. On the other hand, on the TeV brane the unbroken groups are the $U(1)_{B-L}$ and $SU(2)_D$, so that their effect is to mix the SM gauge bosons. In the case of $SU(2)_D$ it is clear that there is a direct contribution to the $S$ parameter, not suppressed by a log. In both cases there will be corrections to $S$, $T$, and $U$ even when the wavefunction is only kept to leading log order. For this reason we will deal with the TeV brane induced terms separately. | 1,260 | hep-ph/0401160 | 3,532,132 | 2,004 | 1 | 22 | false | true | 1 | BRANE |
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