conformal field theory - sergei v ketov

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1、SergeiV.JCetovInstitutftiri%eor~ix&ePbysikUniversitiizHannoverGermanybWorldScientificbSingaporelNewJersey*LondonlHongKong._CPrefaceTheaimofphysicsasascienceistodescribethemostfundamentallawsofNature.Beingthemostfundamental,thephysicallawsaresimultaneouslyth

2、esimplestones.Tobesimpledoesnotmeanhowevertobetrivial.Thesimplicityoffundamentalphysicsexhibitsitselfinfundamentalsymmetryprinciples.Itisthereforefundamentalphysicalsymmetryprinciplesthatweshouldbelookingfor,anditismainlyatheoreticalproblem.Itisveryofteninp

3、hysicsthatunderlyingsymmetriesarehiddenbythecomplexityofactualphysicalphenomena,anditistheobjectiveoftheoreticalphysicstouncoverthem.Takinghighenergyphysicsasanexample,thetheoreticalbasisforourcurrentunder-standingofpropertiesanddynamicsofelementaryparticle

4、sisprovidedbyquantumfield*theory(QFT).AgeneralQFThoweverseemstobetoogeneralforthesepurposes.ItisthegaugeQFTsthatareapparentlydistinguishedindescribingfundamentalphysicalinteractionsofNature.ComparedtoageneralQFT,quantumgaugetheoriesaremuchmorerestrictiveand

5、possessadditionalsymmetries.Thewell-knownachievementsofgaugetheoriesinhighenergyphysicsduringlastdecadesperfectlyillustratethepowerofsymmetryprinciplesinphysics.Thehigheranenergyscale,themoresymmetricbecomeinteractionsamongelementaryparticles.Thisisaclearsi

6、gnofsome(normallybroken)symmetrywhichshouldbeformallyrestoredatinfiniteenergiesorvanishingmasses.Anotherrelevantexampleisprovidedbythetheoryofcriticalphenomena.Itisawell-knownfactthatquitedifferentphysicalsystemsattheircriticalityexhibituniver-salbehaviour.

7、Thisalsoindicatesapresenceofsomeunderlyingfundamentalsymmetry.Itistheconformalsymmetrythatisresponsibleinbothcases.Oneimportantpointshouldhoweverbeemphasized.Benefitsofhavingconformalsymmetryusuallycometrueintvodimensions,wherethissymmetrybecomesinfinite-di

8、mensional.Aninfinitenumberofconservationlawsisresponsibleforanintegrabilityoftwo-dimensionalphysicalsystemspossessingconformalinvariance.Itisthetwo-dimensionalconformalfieldtheory(CFT)thatisactuallyadd