Peskin - Introduction to Quantum Field Theory 2

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1、PartIIRenormalizationChapter8Invitation:UltravioletCutosandCriticalFluctuationsThemainpurposeofPartIofthisbookistodevelopageneraltheoryofrenormalization.Thistheorywillexplaintheoriginofultravioletdivergencesineldtheoryandwillindicatewhenthesedivergencescanberemovedsys-tematically.Itwillalsogive

2、awaytoconvertthedivergencesofFeynmandiagramsfromaproblemintoatool.Wewillapplythistooltostudytheasymptoticlarge-orsmall-momentumbehaviorofeldtheoryamplitudes.Whenwerstencounteredanultravioletdivergenceinthecalculationoftheone-loopvertexcorrectioninSection6.3,itseemedanaberrationthatoughttodisapp

3、earbeforeitcausedustoomuchdiscomfort.InChapter7wesawfurtherexamplesofultraviolet-divergentdiagrams,enoughtoconvinceusthatsuchdivergencesoccurubiquitouslyinFeynmandiagramcomputations.Thusitisnecessaryforanyonestudyingeldtheorytodevelopapointofviewtowardthesedivergences.Mostpeoplebeginwiththebelie

4、fthatanytheorythatcontainsdivergencesmustbenonsense.Butthisviewpointisoverlyrestrictive,sinceitexcludesnotonlyquantumeldtheorybuteventheclassicalelectrodynamicsofpointparticles.Withsomeexperience,onemightadoptamorepermissiveattitudeofpeacefulcoexistencewiththedivergences:Onecanacceptatheorywithd

5、i-vergences,aslongastheydonotappearinphysicalpredictions.InChapter7wesawthatallofthedivergencesthatappearintheone-loopradiativecor-rectionstoelectronscatteringfromaheavytargetcanbeeliminatedbycon-sistentlyeliminatingthebarevaluesofthemassandchargeoftheelectroninfavoroftheirmeasuredphysicalvalues.

6、InChapter10,wewillarguethatalloftheultravioletdivergencesofQED,inallordersofperturbationtheory,canbeeliminatedinthisway.Thus,aslongasoneiswillingtoconsiderthemassandchargeoftheelectronasmeasuredparameters,thepredictionsofQEDperturbationtheorywillalwaysbefreeofdivergences.WewillalsoshowinChapter10

7、thatQEDbelongstoawell-denedclassofeldtheoriesinwhichallultravioletdivergencesareremovedafteraxedsmallnumberofphysicalparametersaretakenfromexperiment.Thesetheories,calledrenormalizablequantumeldtheories,aretheonlyo