 This is contrasted with the "instantons" which are objects localized in the Euclidean spacetime; they don't describe static objects but rather special histories that contribute to various probability amplitudes for processes that appear at one "instant" of time.
Another class of topologically nontrivial configurations are skyrmions, and if you want to see a representative that is really close to your "knots", see a paper about knitted fivebranes in M-theory:
http://arxiv.org/abs/hep-th/9803108
In the quantum theory, objects such as solitons - especially monopoles - may behave indistinguishably from the original quanta. There is sometimes a full symmetry between them - the most famous example is the S-duality of gauge theories in 4 dimensions. Electrically charged particles such as gauginos are exchanged with the magnetic monopoles - solitons - as the coupling $g$ is changed to $1/g$.
All these things, when done properly, still satisfy all the postulates of quantum mechanics such as the nonzero commutators between observables (uncertainty principle). In string theory, topological defects include objects such as D-branes, NS5-branes, and in extra-dimensional theories in general, one also has special "knitted" configurations of the metric such as the Kaluza-Klein monopoles (magnetic monopoles extended in extra dimensions).
Best wishes
Lubos

A:

Actually that's not too far off the mark, although I'm not sure "knot" or "kink" is the best word. Quantum field theory, the best theory we currently have to describe particles, says that particles correspond to excitations of a field, which are kind of like waves in water; you could consider the surface of a pond "excited" whenever it's not flat. Just as with water waves, there's an infinite variety of "shapes" you can have for these excitations. For example, you could have a repeating wave, in which the surface of the water cycles up and down over a large area, or you could have just one wave front that just propagates across the water without spreading out very much. The former case is pretty typical for things like light waves, and the latter case is pretty typical for particles of matter, although technically any kind of field (whether it's the electromagnetic field for light, or a quark field in matter, or whatever) can have any of the different types of excitations.
By the way
This is contrasted with the " instantons " which are objects localized in the Euclidean spacetime; they don't identify inactive objects but rather special history that contribute to various probability amplitude for processes that appear at one " instantaneous " of time. 
 Another class of topologically nontrivial shape are skyrmions, and if you want to see a congressman that is in truth close to your " knots ", see a paper about knitted fivebranes in M - hypothesis: 
 http://arxiv.org/abs/hep-th/9803108 
 In the quantum theory, objects such as solitons - specially monopoles - may behave indistinguishably from the original quanta. There cost sometimes a full isotropy between them - the most celebrated example is the S - duality of gauge hypothesis in 4 dimensions. Electrically charged particles such as gauginos are exchanged with the magnetic monopoles - soliton - as the yoke $ g$ is transfer to $ 1 / g$. 
 All these things, when done properly, still satisfy all the postulates of quantum mechanics such as the nonzero commutators between observables (doubt rationale). In string theory, topological defects admit object such as D - branes, NS5 - branes, and in extra - dimensional theories in general, one also has special " knitted " configuration of the metric such as the Kaluza - Klein monopoles (magnetic monopoles extended in extra dimensions). 
 Best wish 
 Lubos 

 A: 

 Actually that's not too far off the mark, although I'm not sure " knot " or " crick " is the best son. Quantum battlefield theory, the best theory we currently have to describe particles, say that particles correspond to excitations of a field, which are kind of like wave in water; you could consider the surface of a pond " excited " whenever it's not flat. merely as with water wave, there's an infinite variety show of " shapes " you can have for these excitation. For exercise, you could have a repeating wave, in which the surface of the water cycles up and down over a large area, or you could have just one wave battlefront that just propagates across the body of water without spreading out very much. The former case is pretty typical for thing like light waves, and the latter case is pretty typical for particles of topic, although technically any kind of field (whether it's the electromagnetic field for luminosity, or a quark field in matter, or whatever) can have any of the different types of excitations. 
 By the manner
 Thls is contrasted with tht "instantons" whick are oujects mocalizea in the Euclidean spacetime; tyey din't describe static obgects but rather wpecmal histories thef contrlyute fl vaxiius probabiliti amplitudes for processes tfac appear at one "instant" of time.
Anothqr clasx lf topologicaljy npgtribpao configurations are skyrmiona, and ih you want to sre a representative that id rewlly close to your "knots", see q pa[wr about knigted fivebgcnes in M-thgory:
http://arxiv.org/abs/hep-th/9803108
In the qjantuk theory, ovjwctd such as sooitonf - especialln monopmles - msy behave indixtiiguiwhably from the origiial quanta. There is fometimes a full symmetry berwwen tvem - the nosg fzmpua examole is the S-dhality of gquge theories in 4 domqbsions. Electrjcally crarged particles such as gauginos are eqchahged with the magnetic nonopoles - solitons - ws the cotpling $g$ is changed to $1/g$.
All these things, when dona pro'efly, sbill wahisfy all the postulates of quantum mechanics auvh as the nonzerj commutatots brjween observabues (unesrfainty principle). Ij strind theiry, topoljgicsl defects include objects wuch as D-braues, NS5-branes, and in ertra-dimensioual thgories in general, one also har spscial "knittfd" confighfations of the mdtrpc sgch as the Kaluza-Klein monjpoles (majnetie monopoues gxtendeq in extra dimekvions).
Best wishes
Luhos

A:

Aetualny that's nlt too far off the mark, althougi I'm not sure "ktot" or "kink" is tme best word. Quwntum field thgory, the yest tfeory we clrrently iave to descwibe particlev, says that perticles sorrwspobd to ebzitations of a field, whpck are kine of like waves in wajed; you could conwidtr the surface og a pogd "eeciteq" whenever it'v nog fust. Jurt as with cager eaves, there's an infitite variety of "shapes" yju can hqve for ehese excitatoons. For example, ylu conld hate a rrpewting wave, in which the surfacs of the aatcr cycles up wnd eown over a karge area, or you could have just one weve front that just propagates across the cauer without s'readigg out vesy much. The former cqse is pretty typlcal for things like ljght wdves, wnd the latter case is pretty typical for particles of matter, although texhnically any kind of gield (wketker it's the xlectromagnetic fpeld for light, or a quark field mn matter, mr whatever) can have any of thr aifferent typgs of excitations.
By the wag
This is contrasted with the "instantons" which localized the Euclidean they don't describe histories contribute to various amplitudes for processes appear at one "instant" of time. class of topologically nontrivial configurations are skyrmions, and if you want to see representative that is really close to your "knots", see a paper about knitted in http://arxiv.org/abs/hep-th/9803108 the theory, objects such as solitons - especially monopoles - may behave indistinguishably from the original quanta. is sometimes a full symmetry between them - most famous example is S-duality of gauge theories in dimensions. charged particles as are with the magnetic - solitons - as the coupling $g$ is changed to $1/g$. All these things, when done properly, satisfy all of quantum such the commutators between observables In string theory, topological defects include D-branes, NS5-branes, and in extra-dimensional theories in general, also has "knitted" configurations of the metric such the Kaluza-Klein monopoles (magnetic monopoles extended in extra Best wishes Lubos A: Actually that's not too far off the mark, although I'm not or "kink" is the word. Quantum field the theory currently to describe says that particles correspond to excitations of a field, which are of like waves in water; you could consider the surface pond whenever it's not Just as with water there's infinite variety of "shapes" have these you have repeating wave, in which surface of the water cycles and down over a have just one wave front that just propagates the water without spreading out very much. former case is pretty typical for things like light waves, and the case is for particles of matter, although technically any kind field (whether it's the field for light, or a quark field in matter, whatever) have any the different types excitations. By the
 This is contrasted with the "inStantons" whIch arE obJecTs LocaLizeD in the EuclideaN SpacEtime; they don't describe sTatic ObJEcts BUt RatheR speciaL HiSTOriEs ThAt cOnTRiBute tO vaRious prObability aMplItUdes for proceSSeS that appeaR at One "instant" of TimE.
AnothEr ClaSS of toPolOgicaLly nonTRivial ConfiguraTiONs are sKYrmions, AND iF you Want to see a represeNTaTIve that is reallY close To YOuR "KNotS", seE a paper aboUt KnittED fivebrANeS IN m-thEOry:
http://arxiv.oRg/abs/hep-th/9803108
IN The QuantuM tHeoRY, objecTs sucH aS SolItons - especiAlly Monopoles - May behAVe indisTInguishAbly frOm tHe oRigiNAl QuAntA. THEre IS sOmeTImeS a full syMmEtRy betWeen THEM - The mOst FamoUs exaMple is the S-duaLitY of gAUge TheorIes in 4 DimeNsIons. ELectriCally ChArged particles sUch aS gauginos Are ExChaNgEd witH The magNetIc mOnopoleS - solitoNS - as ThE COUpLing $g$ is changed to $1/g$.
ALl THEsE things, wHen donE PrOpERly, still SaTisFy alL THe posTulaTEs Of quantuM mechaNIcS sUch as thE nOnzero CoMmuTatOrs beTWeen ObservAbles (uncErtaiNTy principle). In sTRing theory, topOLoGICaL DefeCts Include objeCts sUCh as d-braNEs, nS5-bRAnes, aNd in eXtRA-dIMensional theories in GeNeral, oNe alsO has special "knItted" confiGURAtions of The mETrIC such as the KaluZa-KleIn monopoleS (Magnetic MonopOles exteNded in extRA DimensioNs).
BEst WisHes
lUBoS

A:

Actually thaT'S Not tOo Far off tHe mArk, althOugH I'm Not SurE "kNot" or "kink" Is the besT wOrD. QUaNtuM fielD Theory, thE bEst ThEorY we cuRRently Have tO desCrIbE ParTicles, sAYs THAt paRtIcLes cOrrEsPond tO excITatIons of a Field, whicH arE Kind Of LiKe waves In water; you couLd Consider thE sUrfAce of a PONd "exciteD" whenever it's not flat. Just AS with waTer Waves, TherE's an infinIte VarietY of "SHapes" yOu can hAve foR tHesE EXcitaTIOnS. FoR eXample, you cOULd hAve a rEpEatiNg wave, iN which the surface of THe wAter cycles up aNd dOwn oVER a LarGE aREa, oR yOU coULD have just one wavE front that JuST pRopagates aCRosS tHe water Without SpreaDIng out vEry much. ThE former caSe Is prETTy tYpical for tHings likE light wavES, and tHE lAtter CasE is preTtY tyPical For parTIclEs of mAtter, aLtHough tEchniCaLly any kiNd of field (whether it's the eLectroMagneTic Field for lIghT, Or a Quark fielD in mAtter, or whaTevEr) cAn havE anY Of the DiffEReNt tYPes of ExciTAtions.
By tHE wAy
 This is contrasted with t he "instan tons"  wh ich  a re o bjec ts localized i n  the  Euclidean spacetime;theydo n 't d e sc ribestatico bj e c tsbu trat he r  s pecia l h istorie s that con tri bu te to variou s  p robability  am plitudes for  pr ocesse stha t  appe arat on e "ins t ant" o f time.
A no t her cl a ss of t o p ol ogic ally nontrivial c o nf i gurations areskyrmi on s ,a n d i f y ou want to  s ee ar epresen t at i v e  th a t is really c lose to you r  "k nots",  s eea  paper  abou tk nit ted fivebra nesin M-theo ry:
ht t p://arx i v.org/a bs/hep -th /98 0310 8 
I nthe  q u ant u mthe o ry,  objects  s uc h assoli t o n s  - e spe cial ly mo nopoles - may  be have ind istin guish ably  f rom t he ori ginal  q uanta. There is  som etimes aful lsym me try b e tweenthe m -  the mo st famo u s e xa m p l eis the S-duality o fg a ug e theori es in4  d im e nsions.El ect rica l l y cha rged pa rticlessuch a s  g au ginos a re  excha ng edwit h the magn etic m onopoles  - so l itons - as the coupling $g$i sc h an g ed t o $ 1/g$.
All t hese thin gs,w he n d o ne pr operl y, st i ll satisfy all thepo stulat es of  quantum mech anics such a s  the non zero co m mutators betwe en ob servables( uncertai nty p rinciple ). In str i n g theory , t opo log ica l de fects include o bjec ts  such a s D -branes , N S5- bra nes ,and in ex tra-dime ns io na lthe ories in gener al , o ne  al so ha s  speci al "k nitt ed "c onf igurati o ns o f th eme tric  su ch  as t he K a luz a-Klein  monopole s ( m agne ti cmonopol es extended i nextra dime ns ion s).
Be s t  wishesLubos

A:

Actually tha t 's nottoo  faroffthe mark,  al though  I' m  not s ure "k not"or  "k i n k" is t he  be st  word. Qua n t umfield  t heor y, thebest theory we cur r ent ly have to de scr ibep a rt icl e s, say st hat p articles corres pond to ex ci t at ions of af iel d,  whichare kin d ofl ike wav es in wat er; you c ou ld c o n sid er the sur face ofa pond "e x cited "  w henev erit's n ot  fl at. J ust as wit h wat er wav es , ther e's a ninfinite  variety of "shapes" yo u canhavefor  these ex cit a tio ns. For e xamp le, you co uld  ha ve arep e ating  wav e ,inw hichthes urface of th e w a t er  cycles upa n d  do wn ov era  large  are a, or you could h a ve just one wa ve f r o nttha t  jus tpropagates acr oss  t h e  water w it hout spread ing outve r y muc h. The  forme r casei s  p r etty t ypic alfor thing s l ik e  lightwa ve s , andthela tter c ase is pret t y  typical for par ticle s of ma t ter , alt ho ugh tec h nica lly any ki nd of field  (whet herit'sthe ele ct romagn eti cfield forl ight, ora qua rk fiel din m att er, or  wha t e ver)canha veany of th e di f fe re n t t ypes  of e xc itat ions.
Byt he way
 This_is contrasted_with the "instantons" which_are objects_localized_in the_Euclidean_spacetime; they don't_describe static objects_but rather special histories_that contribute to_various_probability amplitudes for processes that appear at one "instant" of time.
Another class of topologically_nontrivial_configurations are_skyrmions,_and_if you want to see_a representative that is really_close to_your "knots", see a paper about knitted fivebranes_in_M-theory:
http://arxiv.org/abs/hep-th/9803108
In the quantum_theory, objects such as solitons - especially monopoles -_may behave indistinguishably from the original_quanta. There is_sometimes_a_full symmetry between them_- the most famous example is_the S-duality of gauge theories in_4 dimensions. Electrically charged particles such as_gauginos are exchanged with the magnetic_monopoles - solitons - as_the coupling_$g$ is changed to $1/g$.
All_these things, when_done properly,_still satisfy all_the postulates of quantum mechanics such_as the nonzero_commutators between observables (uncertainty principle). In_string_theory, topological defects_include_objects_such as_D-branes, NS5-branes, and_in_extra-dimensional theories_in_general, one also has special "knitted"_configurations_of the metric such as the Kaluza-Klein_monopoles (magnetic monopoles extended_in_extra dimensions).
Best wishes
Lubos

A:

Actually that's_not too far off the_mark, although I'm not sure "knot"_or "kink"_is the_best word. Quantum field theory, the best theory we currently have_to describe particles, says that particles_correspond to excitations of_a field,_which_are kind of_like_waves in_water; you could consider the surface of_a pond_"excited" whenever it's not flat. Just_as with water waves,_there's_an infinite variety of "shapes" you_can have for these excitations. For_example, you could have a_repeating_wave,_in which the surface of_the water cycles up and down_over a large_area, or you could have just one_wave_front that just propagates across the_water_without spreading out very much. The_former_case_is pretty typical for things_like light waves, and the latter_case is pretty typical for particles of matter, although_technically any kind_of field (whether it's the_electromagnetic_field_for light, or a quark field in matter, or whatever)_can have_any of the_different types of excitations.
By the way