ullin, 2002). A space-time interval is a physical quantity that has a value for each pair of points in space and time; space-time intervals may be considered fields. In the modern parlance of quantum field theory, a field occupies space, contains energy and momentum (mass times velocity), and its presence precludes a classical true vacuum (Wheeler, 1998); fields have such familiar properties as energy content and momentum, just as particles can have (Feynman, 1970). The fact that a field can possess energy and momentum makes it very real. This has led physicists to consider fields as physical entities (particles, objects), making the field concept a supporting paradigm of modern physics. It was the introduction of the special theory of relativity which opened the way for physicists to start thinking of fields as truly independent entities (Weinberg, 1977). In quantum field theory, fields are understood as particles (electrons, protons, photons, etc.), elevating fields to the status of the most fundamental objects in the universe (Weinberg, 1977). Fields can be classified as scalar, vector, or tensor depending on whether the represented physical quantity is a scalar, vector, or tensor, respectively. Within each category (scalar, vector, tensor), a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators. Physicists have found that the notion of a field is of such practical utility in the analysis of force that a field is often considered to be a force (Feynman, 1970). In quantum field theory, a quantum field acts through the release of force carrier particles (messenger particles, intermediate particles) called "bosons" (Oerter, 2006). Each boson represents a quantum (a discrete quantity) of excitation of the relevant quantum field. There is one kind of field for every type of elementary particle (Weinberg, 1993). In quantum field theory, a force between two particles can be described either as the action of a field generated by one particle on the other, or in terms of the exchange of virtual bosons (quanta) between them. There are three conventionally accepted fundamental interactions or forces in quantum field theory (electromagnetic, strong nuclear, weak nuclear). These fundamental interactions (gauge interactions) are not reducible to more basic interactions; the three fundamental interactions result in all the forces we know (Schumm, 2004; Ulaby, 2010). The three, as part of the Standard Model of particle physics, are described as discrete quantum fields, and
ullin, 2002). A space - time interval is a physical measure that have a value for each pair of points in quad and fourth dimension; space - time interval may be think airfield. In the modern parlance of quantum field hypothesis, a field occupies distance, contain energy and momentum (bulk times velocity), and its bearing precludes a classical true void (Wheeler, 1998); fields have such familiar properties as department of energy content and momentum, precisely as particles can have (Feynman, 1970). The fact that a field can own energy and momentum makes it very real. This has led physicists to consider fields as physical entities (particles, objects), making the field concept a supporting paradigm of modern physics. It was the presentation of the special theory of relativity which open the direction for physicists to start thinking of sphere as truly independent entities (Weinberg, 1977). In quantum field hypothesis, fields are understood as particles (electrons, protons, photons, etc .), elevating fields to the status of the most fundamental objects in the population (Weinberg, 1977). Fields can be classify as scalar, vector, or tensor depending on whether the represented physical quantity is a scalar, vector, or tensor, respectively. Within each category (scalar, vector, tensor), a plain can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators. Physicists have discover that the impression of a field is of such practical utility in the analysis of force that a battlefield is often consider to be a force (Feynman, 1970). In quantum sphere theory, a quantum field act through the release of force carrier particles (messenger particles, intermediate particles) called " bosons " (Oerter, 2006). Each boson represents a quantum (a discrete quantity) of excitement of the relevant quantum field. There is one kind of plain for every type of elementary particle (Weinberg, 1993). In quantum field theory, a force between two particles can be described either as the legal action of a field generated by one particle on the other, or in terms of the exchange of virtual bosons (quantum) between them. There cost three conventionally accepted fundamental interactions or forces in quantum field theory (electromagnetic, potent nuclear, weak nuclear). These fundamental interactions (bore interactions) are not reducible to more basic interaction; the three fundamental interactions result in all the effect we know (Schumm, 2004; Ulaby, 2010). The three, as part of the Standard Model of particle physics, are described as discrete quantum fields, and
ullln, 2002). A space-time interval is a physical quantitb that gas a vauue for each pair of points mn space qnd time; space-time intdrvals maj be consudertd fields. In the modern parlancs of xnantum field thgory, a field occupies spaca, zoutains energy and momentum (mass timef velocotj), and its presgnce kresludss a classical true vacuum (Wheeler, 1998); fieldv have such fsmiliar properties as enerhy clntent and momentul, just as pqrtisoes can have (Feynman, 1970). Uhz fact that a field can possess energy and momeutum makes ut vegi real. This ias leq physicists to conshder firlds as physicsl xntiries (particles, objectv), making the field concept d aupporting paraditm of mmdert phhwicr. Iu wes fhe inhrovuction of fhe special theory of relativiuy ryich opened tge way fjr physicists to start thinking of fielgs zs truly independent enrities (Weinberg, 1977). In qoantum fiejd theory, fields are understood as particles (elecdrons, orouokf, phltons, etc.), elevating fields to the status of trs koxt fundamental objects in tje oniverse (Weinbgrg, 1977). Fizmda can be classifief as scwlar, cector, or tenxor depending on whether thw representeb pyysical quantity id a scalar, rector, or trnsor, respectively. Withnn eacg category (dcalar, vedgor, tensor), a fieud ban te either a classical fielq or a quentum field, aepemding jn whether it is characterized by jumbets or xuantum opfrators. Physicists have found tiet the notion ox a field if of xuch practicaj utility in tke analyfis ow force thzt a fixld is often considered tm be a force (Heynman, 1970). Yn qyantym fiela theory, a quanyum field acts throygh the release of fotcs carrier partieuts (messenger paryicues, ijtxrmedydte particlev) caulea "bosovs" (Oerttx, 2006). Cacf boxon represents a quattum (a discrete quantiyy) of excijation of the relevant quantum field. Thege is onx kind of field for every type of elemehtary parhicje (Weinberg, 1993). In wuantum fielb theory, a force between two particles cen be described either qs the action of a yitld generated by oge particne on the other, or ib terms of the exghange of virtual bosohs (quatta) bftween them. There are three conventionally accepted fundamental interactiins or forces in qhantim fivld cheory (qlecvrumagnetic, strong nuclear, weak nuclear). These funvamental ittzractions (gauge interactions) srd not reducibue to more basic interacfions; thr three fundamental interactionx result in all the forccs we knoq (Schhmm, 2004; Ulaby, 2010). The three, as pary of tke Stabdard Midel of particle ohyxigs, are desfribtd aa discrete quantum fields, and
ullin, 2002). A space-time interval is a that a value each pair of space-time may be considered In the modern of quantum field theory, a field space, contains energy and momentum (mass times velocity), and its presence precludes a true vacuum (Wheeler, 1998); fields have such familiar properties as energy content and just particles have 1970). The fact that a field can possess energy and momentum makes it very real. This led physicists to consider fields as physical entities objects), making the field a supporting paradigm of modern It the introduction the theory relativity which opened way for physicists to start thinking of fields as truly independent entities (Weinberg, 1977). In quantum field fields are particles (electrons, photons, elevating to the status most fundamental objects in the universe can be classified as scalar, vector, or tensor on whether represented physical quantity is a scalar, or tensor, respectively. Within each category (scalar, vector, a field can be either a classical field or a quantum field, depending on whether characterized by numbers or operators. Physicists have that notion a is of practical utility in the analysis of force that a field is considered to be a force (Feynman, 1970). In quantum field quantum acts through the of force carrier particles particles, particles) called "bosons" (Oerter, boson a quantity) excitation the relevant quantum field. is one kind of field every type of elementary field theory, a force between two particles can described either as the action of a generated by one particle on the other, or in terms of the of virtual between them. There are three conventionally accepted fundamental or forces in quantum theory (electromagnetic, strong nuclear, weak nuclear). These fundamental interactions interactions) not reducible more basic interactions; three fundamental interactions in all the know (Schumm, Ulaby, The of the Standard Model of particle are as discrete quantum fields, and
ullin, 2002). A space-time interval is A physical qUantiTy tHat HaS a vaLue fOr each pair of poINts iN space and time; space-time InterVaLS may BE cOnsidEred fieLDs. iN The MoDeRn pArLAnCe of qUanTum fielD theory, a fiEld OcCupies space, cONtAins energy And Momentum (mass TimEs veloCiTy), aND its pResEnce pRecludES a clasSical true VaCUum (WheELer, 1998); fielDS HaVe suCh familiar propertIEs AS energy content And momEnTUm, JUSt aS paRticles can HaVe (FeyNMan, 1970). The fACt THAT a fIEld can possess Energy and moMEntUm makeS iT veRY real. THis haS lED phYsicists to cOnsiDer fields As physICal entiTIes (partIcles, oBjeCts), MakiNG tHe FieLd COncEPt A suPPorTing paraDiGm Of modErn pHYSICs. It Was The iNtrodUction of the spEciAl thEOry Of relAtiviTy whIcH openEd the wAy for PhYsicists to start ThinKing of fieLds As TruLy IndepENdent eNtiTieS (WeinbeRg, 1977). In quaNTum FiELD ThEory, fields are underStOOD aS particlEs (elecTRoNs, PRotons, phOtOns, Etc.), eLEVatinG fieLDs To the staTus of tHE mOsT fundamEnTal objEcTs iN thE univERse (WEinberG, 1977). Fields cAn be cLAssified as scalAR, vector, or tensOR dEPEnDIng oN whEther the repReseNTed pHysiCAl QuaNTity iS a scaLaR, VeCTor, or tensor, respectiVeLy. WithIn eacH category (scalAr, vector, teNSOR), a field cAn be EItHEr a classical fiEld or A quantum fiELd, dependIng on Whether iT is characTERized by nUmbErs Or qUanTUM oPerators. PhysiCISts hAvE found tHat The notiOn oF a fIelD is Of Such practIcal utilItY iN tHe AnaLysis OF force thAt A fiElD is Often COnsideRed to Be a fOrCe (fEynMan, 1970). In quANtUM FielD tHeOry, a QuaNtUm fieLd acTS thRough thE release oF foRCe caRrIeR particLes (messenger pArTicles, inteRmEdiAte parTICles) callEd "bosons" (Oerter, 2006). Each boson REpresenTs a QuantUm (a dIscrete quAntIty) of eXciTAtion oF the reLevanT qUanTUM fielD. tHeRe iS oNe kind of fiELD foR everY tYpe oF elemenTary particle (WeinbeRG, 1993). In Quantum field tHeoRy, a fORCe BetWEeN Two PaRTicLES can be described Either as thE aCTiOn of a field GEneRaTed by onE particLe on tHE other, oR in terms oF the exchaNgE of vIRTuaL bosons (quaNta) betweEn them. TheRE are tHReE convEntIonallY aCcePted fUndameNTal InterActionS oR forceS in quAnTum field Theory (electromagnetic, stRong nuClear, WeaK nuclear). THesE FunDamental iNterActions (gauGe iNteRactiOns) ARe not ReduCIbLe tO More bAsic INteractioNS; tHe tHREe Fundamental INTEraCtionS reSUlt in aLl thE forces we know (SchuMM, 2004; Ulaby, 2010). The three, As paRT Of tHe STAndaRd model of particlE phYsICS, are descRiBed as discreTe quantuM fIElds, aNd
ullin, 2002). A space-time  intervalis aphy sic al  qua ntit y that has a v a luefor each pair of point s insp a ce a n dtime;  space- t im e int er va lsma y  b e con sid ered fi elds. In t hemo dern parlanc e  o f quantumfie ld theory, a  fi eld oc cu pie s  spac e,conta ins en e rgy an d momentu m( mass t i mes vel o c it y),and its presencep re c ludes a classi cal tr ue va c u um(Wh eeler, 199 8) ; fie l ds have su c h fam i liar properti es as energ y  co ntentan d m o mentum , jus ta s p articles ca n ha ve (Feynm an, 19 7 0). The fact th at a f iel d c an p o ss es s e ne r gya nd  mo m ent um makes  i tveryreal . T h is h asledphysi cists to cons ide r fi e lds  as p hysic al e nt ities  (part icles ,objects), makin g th e field c onc ep t a  s uppor t ing pa rad igm  of mod ern phy s ics .I t wa s the introduction  o f th e specia l theo r yof relativi ty  wh icho p enedthew ay  for phy sicist s  t ostart t hi nkingof  fi eld s ast ruly  indep endent e ntiti e s (Weinberg, 1 9 77). In quant u mf i el d  the ory , fields ar e un d erst ooda spar t icles  (ele ct r on s , protons, photons,  e tc.),eleva ting fields t o the stat u s of the m ostf un d amental object s inthe univer s e (Weinb erg,1977). F ields can b e classi fie d a s s cal a r ,vector, or te n s or d ep endingonwhether  th e r epr ese nt ed physic al quant it yis  a  sc alar, vector,or  te ns or,  resp e ctivel y. Wi thin  e ac h  ca tegory( sc a l ar,ve ct or,ten so r), a  fie l d c an be e ither a c las s ical  f ie ld or a  quantum fiel d,  depending  o n w hether i t is cha racterized by numbers o r  quantu m o perat ors.  Physicis tshave f oun d  thatthe no tionof  af i eld i s of  su ch  practical u til ity i ntheanalysi s of force that af iel d is often co nsi dere d to  be af orc e( Fey n m an, 1970). In q uantum fie ld th eory, a qu a ntu mfield a cts thr ought he rele ase of fo rce carri er  par t i cle s (messeng er parti cles, int e rmedi a te  part icl es) ca ll ed"boso ns" (O e rte r, 20 06). E ac h boso n rep re sents aquantum (a discrete qua ntity)  of e xci tation of  th e  re levant qu antu m field. T her e i s one  ki n d offiel d  f ore verytype of elemen t ar y p a r ti cle (Weinbe r g ,  19 93).Inq uantum  fie ld theory, a forc e  between two p arti c l escan be d es cribed eitherasth e action o fa field gen erated b yo ne pa rticle  on th e other , or in ter ms o f t he exchan geof virtual  b os o ns (qu anta )betwee n them .  The r e  are three conve ntion a l ly ac c ept ed fu nd amental inte ractions o r forces in  quant um f ieldtheory(e lectro mag ne tic, stron g  nuclear,  weak  nuclea r) . Th ese  funda ment a l  inte ract io ns(gauge in t e ra c ti on s ) a re n ot re du cibl e to more basic in ter a ctions;  t het h ree fu n da m e ntal inter act ionsr e sult in al l  the fo r ces w e know  (Schu mm, 200 4 ; U la by, 201 0). T he three,  as parto f t he  Sta ndard Mo de l of  p art ic le physics, are  describ ed as di s c rete q uan t um f i elds,an d
ullin, 2002)._A space-time_interval is a physical_quantity that_has_a value_for_each pair of_points in space_and time; space-time intervals_may be considered_fields._In the modern parlance of quantum field theory, a field occupies space, contains energy_and_momentum (mass_times_velocity),_and its presence precludes a_classical true vacuum (Wheeler, 1998);_fields have_such familiar properties as energy content and momentum,_just_as particles can_have (Feynman, 1970). The fact that a field can_possess energy and momentum makes it_very real. This_has_led_physicists to consider fields_as physical entities (particles, objects), making_the field concept a supporting paradigm_of modern physics. It was the introduction_of the special theory of relativity_which opened the way for_physicists to_start thinking of fields as_truly independent entities_(Weinberg, 1977)._In quantum field_theory, fields are understood as particles_(electrons, protons, photons,_etc.), elevating fields to the status_of_the most fundamental_objects_in_the universe_(Weinberg, 1977). Fields_can_be classified_as_scalar, vector, or tensor depending on_whether_the represented physical quantity is a scalar,_vector, or tensor, respectively._Within_each category (scalar, vector,_tensor), a field can be_either a classical field or a_quantum field,_depending on_whether it is characterized by numbers or quantum operators. Physicists have_found that the notion of a_field is of such_practical utility_in_the analysis of_force_that a_field is often considered to be a_force (Feynman,_1970). In quantum field theory, a_quantum field acts through_the_release of force carrier particles (messenger_particles, intermediate particles) called "bosons" (Oerter,_2006). Each boson represents a_quantum_(a_discrete quantity) of excitation of_the relevant quantum field. There is_one kind of_field for every type of elementary particle_(Weinberg,_1993). In quantum field theory, a_force_between two particles can be described_either_as_the action of a field_generated by one particle on the_other, or in terms of the exchange of virtual_bosons (quanta) between_them. There are three conventionally_accepted_fundamental_interactions or forces in quantum field theory (electromagnetic, strong nuclear,_weak nuclear)._These fundamental interactions_(gauge interactions) are not reducible to more basic interactions; the_three fundamental interactions result in all the_forces we know (Schumm, 2004; Ulaby, 2010). The three, as part_of the Standard Model of particle physics, are_described as discrete quantum fields, and