Renormalization and effective field theory book Kevin Costello

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1、RenormalizationandEffectiveFieldTheoryKevinCostelloThisisapreliminaryversionofthebookRenormalizationandEffectiveFieldTheorypublishedbytheAmericanMathematicalSociety(AMS).ThispreliminaryversionismadeavailablewiththepermissionoftheAMSandmaynotbechanged,edited,orreposted

2、atanyotherwebsitewithoutexplicitwrittenpermissionfromtheauthorandtheAMS.Author'spreliminaryversionmadeavailablewithpermissionofthepublisher,theAmericanMathematicalSocietyContentsChapter1.Introduction11.Overview12.Functionalintegralsinquantumfieldtheory43.Wilsonianlowen

3、ergytheories64.AWilsoniandefinitionofaquantumfieldtheory135.Locality136.Themaintheorem167.Renormalizability198.Renormalizablescalarfieldtheories219.Gaugetheories2310.Observablesandcorrelationfunctions2711.Otherapproachestoperturbativequantumfieldtheory27Acknowledgements29

4、Chapter2.Theories,Lagrangiansandcounterterms311.Introduction312.Theeffectiveinteractionandbackgroundfieldfunctionalintegrals323.GeneralitiesonFeynmangraphs344.Sharpandsmoothcut-offs425.SingularitiesinFeynmangraphs446.ThegeometricinterpretationofFeynmangraphs477.Adefinitio

5、nofaquantumfieldtheory538.Analternativedefinition559.ExtractingthesingularpartoftheweightsofFeynmangraphs5710.Constructinglocalcounterterms6211.Proofofthemaintheorem.6712.Proofoftheparametrixformulationofthemaintheorem6913.Vector-bundlevaluedfieldtheories7114.Fieldtheori

6、esonnon-compactmanifolds81Chapter3.FieldtheoriesonRn911.Somefunctionalanalysis922.ThemaintheoremonRn993.Vector-bundlevaluedfieldtheoriesonRn1044.HolomorphicaspectsoftheoriesonRn107Chapter4.Renormalizability1133Author'spreliminaryversionmadeavailablewithpermissionofthep

7、ublisher,theAmericanMathematicalSociety4CONTENTS1.Thelocalrenormalizationgroupflow1132.TheKadanoff-Wilsonpictureandasymptoticfreedom1223.Universality1254.Calculationsin4theory1265.Proofsofthemaintheorems1316.Generalizationsofthemaintheorems135Chapter5.Gaugesymmetryandth

8、eBatalin-Vilkoviskyformalism1391.Introduction1392.AcrashcourseintheBatalin-Vilkoviskyformalism1413.TheclassicalBVformalismin