introduction to gauge theories

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1、INTRODUCTIONTOGAUGETHEORIESC.BECCHIDipartimentodiFisica,UniversitadiGenova,IstitutoNazionalediFisicaNucleare,SezionediGenova,viaDodecaneso33,16146Genova(Italy)AbstractTheselecturespresentanelementaryintroductiontoquantumgaugeelds.Therstaimistoshowhow,inthetreeapproximation,gaugeinvariancefollowsf

2、romcovarianceandunitarity.ThisleadstothestandardconstructionoftheLagrangianbymeansofcovariantderivativesinaformthatuniesthemassiveandthemasslesscase.Havingsoidentiedtheclassicaltheory,theFaddeev-Popovquanti-zationmethodisintroducedandtheBRSinvarianceoftheresultingactionisdiscussed.arXiv:hep-ph/970

3、5211v12May199711LecturesgivenattheTriangleGraduateSchool96,CharlesUniversity,PragueSeptem-ber2-11,199611IntroductionTherecentdevelopmentsinhighenergyphysicshaveputgreatem-phasisongaugetheories;indeedthegeneraltheoryoffundamentalinteractionsiscompletelyformulatedinthisframework.Theimpor-tanceoftherol

4、eofgaugeinvariancehasobscuredthereasonsthathavehistoricallyjustiedtheintroductionandthedevelopmentofgaugetheoriesasconsistenteldtheories.Indeedtheyareveryof-tenjustiedonthebasisofa"symmetryprinciple"thathastobeacceptedasafundamentalprincipleinnature.Asamatteroffactgreatcollectiveeortshavebeennee

5、dedtoidentifygaugetheoriesasthenatural,andinasenseunique,quan-tumtheoriesofvectorelds.Itistheprimaryroleofvectorcurrentshidingassociatevectoreldsandtheensuingdiscoveryofthecorre-spondingbosonsthathasputgaugetheoriesintheiractualpreeminentpositioninHighEnergyPhysics.Theprogressesintheunderstand-ing

6、ofthefundamentalnatureofstronginteractionsisalsobasedongaugetheoriesinspiteofthelackofassociateobservablechargesandvectorparticles.Thehypothesisofconnementhasinfactextendedtherangeofgaugetheoriesopeningthepossibilitythatthevectoreldsgiveanadequatedescriptiononlyoftheshortdistanceprop-ertiesofstron

7、ginteractions[1].Theyshouldremainingunobservabletogetherwiththeassociatedchargessinceatlargetimesanddistancestheirpresenceishiddenbyacatastrophicgrowthofthestrengthofthecoupling,.Inspiteofthelackofvec