A novel renormalizable representation of the Yang-Mills theory

A novel renormalizable representation of the Yang-Mills theory

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时间:2019-05-27

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1、AnovelrenormalizablerepresentationoftheYang-MillstheoryAndreiYu.Dubin1ITEP,B.Cheremushkinskaya25,Moscow117259,RussiaAbstractForagenericgauge-invariantcorrelatorA,wereformulatethestandardD=4Yang-Millstheoryasarenormalizablesystemoftwointeractingfiel

2、dsaµandBµwhichfaithfullyrepresenthigh-andlow-energydegreesoffreedomofthesinglegaugefieldAµintheoriginalformulation.Itopensapossibilitytosynthesizeaninfrared-nonsingularweak-couplingseries,employedtointegrateoveraµforagivenbackgroundBµ,withqualitativelydiff

3、erentmethods.Thesemethodsaretobeappliedtoevaluatetheresulting(aftertheaµ−integration)representationofAintermsofgauge-invariantgenericallynon-locallow-energyobservables,likeWilsonloops.ThelatterobservablesareaveragedoverBµwithrespecttoagauge-invari

4、antWilsoneaneffectiveactionSeff[B].Toavoidadestructivedissipationbetweenthehigh-andlow-energyexcitations,weimplementaspecificfine-tuningoftheinteractionbetweenthepairofthefields:priortotheintegrationoverBµ,theexpectationvalueavanishes,inthetreeorderofthe

5、loop-wiseexpansion,foranarbitraryconfigurationofBµ.Keywords:Yang-Mills,Wilsoneanaction,gaugeinvariancearXiv:0706.4051v1[hep-th]27Jun20071e-mail:dubin@itep.ru11IntroductionTheD=4dimensionalSU(N)Yang-Millstheory(YMD),definedbytheactionZD22SYM[Aµ]=dxtrFµν(A

6、)/4g,(1.1)belongstoaclassofthesystemswherethephysicsatshortdistances,characterizedbyasymptoticfreedom,isqualitativelydifferentcomparedtothelow-energyphysicsgovernedbyconfinement.Therefore,itisreasonabletosearchforaformalismwhichallowstoeffectivelycombinediff

7、erentcomputationaltechniquesappliedrespectivelytothehigh-andlow-energydynamicsinterpolatedatascaleΛsufficientlylargerthan2Λ.intYMThegoodoldweak-couplingseriesareknowntobewell-definedonlyintheultraviolet(UV)−1domainofrelativedistancessufficientlysmallerthanΛYM

8、.IntheUVdomain,theseriescanbeextendedincludinganinputoftheinfrared(IR)dynamicsofthesystem.Forthispurpose,theonlytheoreticalmethodsofaristheoperatorproductexpansion(OPE).Variousimplementa-tionsofOPEsynthesizetheweak-couplin

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