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1、SergeiV.HannoverGermanyWorldScientificSingaporelNewJersey*LondonlHongKongCPrefaceTheaimofphysicsasascienceistodescribethemostfundamentallawsofNature.Beingthemostfundamental,thephysicallawsaresimultaneouslythesimplestones.Tobesimpledoesnotmeanhowevertobetrivial.Thesimplicityoff
2、undamentalphysicsexhibitsitselfinfundamentalsymmetryprinciples.Itisthereforefundamentalphysicalsymmetryprinciplesthatweshouldbelookingfor,anditismainlyatheoreticalproblem.Itisveryofteninphysicsthatunderlyingsymmetriesarehiddenbythecomplexityofactualphysicalphenomena,anditisthe
3、objectiveoftheoreticalphysicstouncoverthem.Takinghighenergyphysicsasanexample,thetheoreticalbasisforourcurrentunder-standingofpropertiesanddynamicsofelementaryparticlesisprovidedbyquantumtheory(QFT).AgeneralQFThoweverseemstobetoogeneralforthesepurposes.Itisthegaugethatareappar
4、entlydistinguishedindescribingfundamentalphysicalinteractionsofNature.ComparedtoageneralQFT,quantumgaugetheoriesaremuchmorerestrictiveandpossessadditionalsymmetries.Thewell-knownachievementsofgaugetheoriesinhighenergyphysicsduringlastdecadesperfectlyillustratethepowerofsymmetr
5、yprinciplesinphysics.Thehigheranenergyscale,themoresymmetricbecomeinteractionsamongelementaryparticles.Thisisaclearsignofsome(normallybroken)symmetrywhichshouldbeformallyrestoredatinfiniteenergiesorvanishingmasses.Anotherrelevantexampleisprovidedbythetheoryofcriticalphenomena.
6、Itisawell-knownfactthatquitedifferentphysicalsystemsattheircriticalityexhibituniver-salbehaviour.Thisalsoindicatesapresenceofsomeunderlyingfundamentalsymmetry.Itistheconformalsymmetrythatisresponsibleinbothcases.Oneimportantpointshouldhoweverbeemphasized.Benefitsofhavingconfor
7、malsymmetryusuallycometrueindimensions,wherethissymmetrybecomesdimensional.Aninfinitenumberofconservationlawsisresponsibleforanintegrabilityoftwo-dimensionalphysicalsystemspossessingconformalinvariance.Itisthedimensionalfieldtheory(CFT)thatisactuallyaddressedinthisbook.CFTisvi
8、ewedasaspecificQFThavingconformalsymmetryanditsowngeneralprin
