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1、NEWLi%tIR4NGIAN4I)d4iii1ILFONI41INfHEUriYG.GiachettaL.MangiarottiG.SardanashviI3WorldScientificNEWLAGRANGIANANDHAMILTONIANMETHODSINFIELDTHEORYNEWLAGRANGIANANDHAMILTONIANMETHODSINFIELDTHEORYG.GiachettaUniv.CamertnoL.MangiarottiUnivCamerinoG.SardanashvilyMoscowStateUniv.WorldScie
2、ntificSingapore*HongKongPublishedbyWorldScientificPublishingCo.Pte.Ltd.POBox128,FarrerRoad,Singapore912805USAoffice:Suite1B,1060MainStreet,RiverEdge,NJ07661UKoffice:57SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbook
3、isavailablefromtheBritishLibrary.NEWLAGRANGIANANDHAMILTONIANMETHODSINFIELDTHEORYCopyright®1997byWorldScientificPublishingCo.Pte.Ltd.Allrightsreserved.Thisbookorpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinform
4、ationstorageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfromt
5、hepublisher.ISBN981-02-1587-8Thisbookisprintedonacid-freepaper.PrintedinSingaporebyUto-PrintPrefaceThisbookaddressestheapplicationofjetmanifoldformalismtocontemporaryclassicalfieldtheory.Thisisthenaturaldevelopmentofthewell-knowngeometricformulationoffieldtheory,whereclassicalf
6、ieldsarerepresentedbysectionsoffibredmanifolds.Inmathematics,thetheoryofdifferentialoperatorsandthecalculusofvariationsareexpressedintermsofjetmanifold,which,infieldtheory,providetheadequatemathematicallanguageforLagrangianandHamiltonianformalisms.Ingeneral,thebookconsidersonly
7、firstorderLagrangianandHamiltoniansystemsbecausemostcontemporaryfieldmodelsareofthistype.Twomainpeculiaritiesofthejetformulationoffieldtheoryshouldbeempha-sized.Firstly,jetsoffibredmanifolds(whensectionsareidentifiedbyafinitenumberoftermsoftheirTaylorseries)formsmoothfinite-dim
8、ensionalmanifolds.There-fore,thedynamicsoffieldsystems
