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1、advancedclassicalfieldtheoryThispageintentionallyleftblankadvancedclassicalfieldtheorygiovannigiachettauniversityofcamerino,italyluigimangiarottiuniversityofcamerino,italygennadisardanashvilymoscowstateuniversity,russiaWorldScientificNEWJERSEY•LONDON•SINGAPORE
2、•BEIJING•SHANGHAI•HONGKONG•TAIPEI•CHENNAIPublishedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLink,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UKoffice:57SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-Publicat
3、ionDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.ADVANCEDCLASSICALFIELDTHEORYCopyright©2009byWorldScientificPublishingCo.Pte.Ltd.Allrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includin
4、gphotocopying,recordingoranyinformationstorageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,U
5、SA.Inthiscasepermissiontophotocopyisnotrequiredfromthepublisher.ISBN-13978-981-283-895-7ISBN-10981-283-895-3PrintedinSingapore.RokTing-AdvClassicalFieldTheory.pmd19/29/2009,9:54AMJanuary26,20092:48WorldScientificBook-9inx6inbook08PrefaceContemporaryquantumfieldt
6、heoryismainlydevelopedasquantizationofclassicalfields.Classicalfieldtheorythusisanecessarysteptowardsquan-tumfieldtheory.ThisbookprovidesanexhaustmathematicalfoundationofLagrangianclassicalfieldtheoryanditsBRSTextensionforthepurposeofquantization.Lagrangiantheoryo
7、fGrassmann-graded(evenandodd)fieldsonfibrebundlesandgradedmanifoldsispresentedinthebookinaverygeneralsetting.Itisadequatelyformulatedingeometricandalgebraictopologicaltermsofthejetmanifoldsandthevariationalbicomplex.Themainingre-dientsinthisformulationarecohomol
8、ogyofthevariationalbicomplex,theglobalfirstvariationalformula,variationalsymmetriesandsupersymme-tries,thefirstNoethertheorem,Noetheridentities,thedirectandinversesecondNoethertheore
