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1、LectureNotesinMathematics1887Editors:J.-M.Morel,CachanF.Takens,GroningenB.Teissier,ParisK.Habermann·L.HabermannIntroductiontoSymplecticDiracOperatorsABCAuthorsKatharinaHabermannStateandUniversityLibraryGttingenöPlatzderGttingerSiebenö137073GöttingenGermanye-mail:habermann@sub.
2、uni-goettingen.deLutzHabermannDepartmentofMathematicsUniversityofHannoverWelfengarten130167HannoverGermanye-mail:habermann@math.uni-hannover.deLibraryofCongressControlNumber:2006924i23MathematicsSubjectClassification(2000):53-02,53Dxx,58-02,58JxxISSNprintedition:0075-8434ISSNel
3、ectronicedition:1617-9692ISBN-103-540-33420-3SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-33420-0SpringerBerlinHeidelbergNewYorkDOI10.1007/b138212Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslatio
4、n,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemust
5、alwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessMediaspringer.comcSpringer-VerlagBerlinHeidelberg2006PrintedinTheNetherlandsTheuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthisp
6、ublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:bytheauthorsandSPIPublisherServicesusingaSpringerLATEXpackageCoverdesign:design&productionGmbH,HeidelbergPrinte
7、donacid-freepaperSPIN:11736684VA41/3100/SPI543210ToKarenPrefaceThisbookaimstogiveasystematicandself-containedintroductiontothetheoryofsymplecticDiracoperatorsandtoreflectthecurrentstateofthesubject.Atthesametime,itisintendedtoestablishtheideathatsymplec-ticspingeometryandsymple
8、cticDiracoperatorsmaygivevaluabletoolsinsymplecticgeometryand