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1、ThispageintentionallyleftblankDIFFERENTIALGEOMETRYANDLIEGROUPSFORPHYSICISTSDifferentialgeometryplaysanincreasinglyimportantroleinmoderntheoreticalphysicsandappliedmathematics.Thistextbookgivesanintroductiontogeometricaltopicsusefulintheoreticalphysicsandappliedmathematics,includingmanifolds,
2、tensorfields,differentialforms,connections,symplecticgeometry,actionsofLiegroups,bundlesandspinors.Havingwrittenitinaninformalstyle,theauthorgivesastrongemphasisondevelopingtheunderstandingofthegeneraltheorythroughmorethan1000simpleexercises,withcompletesolutionsordetailedhints.Thebookwillpre
3、parereadersforstudyingmoderntreatmentsofLagrangianandHamiltonianmechanics,electromagnetism,gaugefields,relativityandgravitation.DifferentialGeometryandLieGroupsforPhysicistsiswellsuitedforcoursesinphysics,mathematicsandengineeringforadvancedundergraduateorgraduatestudents,andcanalsobeusedfora
4、ctiveself-study.Therequiredmathematicalbackgroundknowledgedoesnotgobeyondthelevelofstandardintroductoryundergraduatemathematicscourses.MarianFecko´,currentlyattheDepartmentofTheoreticalPhysics,ComeniusUni-versity,Bratislava,SlovakiaandattheInstituteofPhysics,SlovakAcademyofSciences,Bratislav
5、a,worksonapplicationsofdifferentialgeometryinphysics.Hehasover15years’experiencelecturingonmathematicalphysicsandteachingcoursesondifferentialgeometryandLiegroups.DIFFERENTIALGEOMETRYANDLIEGROUPSFORPHYSICISTSMARIANFECKO´ComeniusUniversity,Bratislava,SlovakiaandSlovakAcademyofSciences,Bratisl
6、ava,SlovakiacambridgeuniversitypressCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SãoPauloCambridgeUniversityPressTheEdinburghBuilding,Cambridgecb22ru,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780
7、521845076©M.Fecko2006Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublishedinprintform
