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1、Quantum®eldtheoryFrankWilczek*InstituteforAdvancedStudy,SchoolofNaturalScience,Princeton,NewJersey08540Theauthordiscussesthegeneralprinciplesunderlyingquantum®eldtheoryandattemptstoidentifyitsmostprofoundconsequences.Thedeepestoftheseconsequencesresultfromthein®nitenumberofdegreesoffreedo
2、minvokedtoimplementlocality.Afewofquantum®eldtheory'smoststrikingsuccesses,bothachievedandprospectivearementioned,andpossiblelimitationsofthetheoryareviewedinthelightofitshistory.[S0034-6861(99)01102-2]I.SURVEYmalizationgroup,effective®eldtheory,solitons,instan-tons,andfractionalchargeand
3、statistics.Quantum®eldtheoryistheframeworkinwhichtheItisclear,fromalltheseexamples,thatquantum®eldregnanttheoriesoftheelectroweakandstronginterac-theoryoccupiesacentralpositioninourdescriptionoftions,whichtogetherformthestandardmodel,arefor-Nature.Itprovidesbothourbestworkingdescriptionof
4、mulated.Quantumelectrodynamics(QED),besidesfundamentalphysicallawsandafruitfultoolforinvesti-providingacompletefoundationforatomicphysicsandgatingthebehaviorofcomplexsystems.Buttheenu-merationofexamples,howevertriumphal,servesmorechemistry,hassupportedcalculationsofphysicalquan-toposethan
5、toanswermorebasicquestions:Whataretitieswithunparalleledprecision.Theexperimentallytheessentialfeaturesofquantum®eldtheory?Whatmeasuredvalueofthemagneticdipolemomentofthedoesquantum®eldtheoryaddtoourunderstandingofmuon,theworld,thatwasnotalreadypresentinquantumme-~g22!5233184600~1680!3102
6、11,(1)chanicsandclassical®eldtheoryseparately?mexpThe®rstquestionhasnosharpanswer.Theoreticalforexample,shouldbecomparedwiththetheoreticalphysicistsarevery¯exibleinadaptingtheirtools,andnopredictionaxiomizationcankeepupwiththem.However,Ithinkit211isfairtosaythatthecharacteristic,coreideas
7、ofquan-~gm22!theor5233183478~308!310(2)tum®eldtheoryaretwofold.First,thatthebasicdy-(seethearticlebyHughesandKinoshitainthisvol-namicaldegreesoffreedomareoperatorfunctionsofume).spaceandtimeÐquantum®elds,obeyingappropriateInquantumchromodynamics(QCD)wecannot,forcomm
