Resolution of the Landau pole problem in QED

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1、DESY97–258FUB-HEP/97–07HUB-HEP–97/56September19971ResolutionoftheLandaupoleprobleminQED∗M.G¨ockelera,R.Horsleyb,V.Linkec,P.Rakowd,G.Schierholzd,eandH.St¨ubenfaInstitutf¨urTheoretischePhysik,Universit¨atRegensburg,D-93040RegensburgbInstitutf¨urPhysik,HumboldtUniversit¨

2、atzuBerlin,D-10115BerlincInstitutf¨urTheoretischePhysik,FreieUniversit¨atBerlin,D-14195BerlindDeutschesElektronenSynchrotronDESY,Institutf¨urHochenergiephysikundHLRZ,D-15735ZeutheneDeutschesElektronenSynchrotronDESY,D-22603HamburgfKonrad-Zuse-Zentrumf¨urInformationste

3、chnikBerlin,D-14195BerlinWepresentnewnumericalresultsfortherenormalizedmassandcouplinginnon-compactlatticeQEDwithstaggeredfermions.ImplicationsforthecontinuumlimitandtheroleoftheLandaupolearediscussed.1.INTRODUCTIONonthelatticeusingnon-compactgauge-fieldsanddynamicalst

4、aggeredfermions[2,3].Inthe1950sLandauinvestigatedtherelationInthistalkwereportonnewmeasurementsbetweenthebarechargeeandtherenormalizedoftherenormalizedmassandcharge.ThischargeeRinQED.Hefound[1]wasstartedin[2]andisnowextendedtolat-ticesofsize164andbaremassesamdownto11N

5、fΛe2−e2=6π2lnm,(1)0.005(adenotesthelatticespacing).UsingRRourmeasurementswehavedeterminedfunctionswhereΛisthemomentumcutoff,mistherenor-am(e2,am)ande2(e2,am).ThesefunctionsRRRmalizedmassoftheelectronandNfisthenum-implythatthetheoryistrivial.Theyalsogiveaberofflavours(fo

6、rstaggeredfermionsNf=4).resolutionoftheLandaupoleproblem.Itiswellknownthat(1)impliestwopotentialproblemswhenΛ→∞:2.THERENORMALIZEDMASSarXiv:hep-lat/9801004v16Jan1998•Wheneisfixedthetheoryhasatrivialcon-Therenormalizedmasswasobtainedfromfitstinuumlimit,i.e.,eR→0.totheferm

7、ionpropagatorasexplainedin[2].TogetamRasafunctionofamandeweneedto•WheneR>0isfixedebecomessingularatknowtheequationofstatewhichrelatesthebareΛ=mexp(6π2/Ne2).Thissingu-parameterstothechiralcondensateσ≡a3hχχ¯i.LandauRfRlarityiscalledtheLandaupole.In[3]wehavefoundthattheσd

8、ataobeyameanfieldequationofstatewithlogarithmiccorrec-Theseproblemsdonotaffectthephenomenolog-tionsicalsuccessofQEDbecauseinpr