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1、ProgressinMathematicalPhysicsVolume53Editors-in-ChiefAnneBoutetdeMonvel,UniversitéParisVIIDenisDiderotGeraldKaiser,TheVirginiaCenterforSignalsandWaves,AustinTexas,USAEditorialBoardSirM.Berry,UniversityofBristol,UKC.Berenstein,UniversityofMaryland,CollegePark,USAP.Blanchard,University
2、ofBielefeld,GermanyA.S.Fokas,UniversityofCambridge,UKD.Sternheimer,UniversitédeBourgogne,Dijon,FranceC.Tracy,UniversityofCalifornia,Davis,USAQuantumSpacesPoincaréSeminar2007BertrandDuplantierVincentRivasseauEditorsBirkhäuserVerlagBaselBostonBerlinEditors:BertrandDuplantierVincentRiva
3、sseauServicedePhysiqueThéoriqueLaboratoiredePhysiqueThéoriqueOrmedesMerisiersUniversitéParisXICEA-Saclay91405OrsayCedex91191Gif-sur-YvetteCedexFranceFrancee-mail:Vincent.Rivasseau@th.u-psud.fre-mail:bertrand.duplantier@cea.fr2000MathematicsSubjectClassification:81V70,81R50,81R60,81T7
4、5,81T17,82B23LibraryofCongressControlNumber:2007933916BibliographicinformationpublishedbyDieDeutscheBibliothekDieDeutscheBibliothekliststhispublicationintheDeutscheNationalbibliogra¿e;detailedbiblio-graphicdataisavailableintheInternetat.ISBN978-3-7643-8521-7Birkhäu
5、serVerlag,Basel–Boston–BerlinThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,speci¿callytherightsoftranslation,reprinting,re-useofillustrations,broadcasting,repro-ductiononmicro¿lmsorinotherways,andstorageindatabanks.Foranykindofusewhat
6、soever,permissionfromthecopyrightownermustbeobtained.©2007BirkhäuserVerlag,P.O.Box133,CH-4010Basel,SwitzerlandPartofSpringerScience+BusinessMediaPrintedonacid-freepaperproducedofchlorine-freepulp.TCF∞PrintedinGermanyISBN987-3-7643-8521-7e-ISBN978-3-7643-8522-4987654321www.birkhauser.
7、chContentsForeword..................................................................xiV.PasquierQuantumHallEffectandNon-commutativeGeometry1Introduction..........................................................12LowestLandaulevelphysics..........................................32.1.Si
8、ngleparticle
