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1、GRADUATESTUDENTSERIESINPHYSICSSeriesEditor:ProfessorDouglasFBrewer,MA,DPhilEmeritusProfessorofExperimentalPhysics,UniversityofSussexSYMMETRIESINQUANTUMMECHANICSFROMANGULARMOMENTUMTOSUPERSYMMETRYMASUDCHAICHIANDepartmentofPhysics,UniversityofHelsinkiandHelsinkiInstituteofPhysicsROLF
2、HAGEDORNRetiredStaffMemberofTheoryDivision,CERN,GenevaINSTITUTEOFPHYSICSPUBLISHINGBristolandPhiladelphiaCONTENTSPrefacexiii1Introduction11.1Notation11.2Somebasicconceptsinquantummechanics41.3Somebasicobjectsofgrouptheory71.3.1Groups:finite,infinite,continuous,Abelian,non-Abelian;s
3、ubgroupofagroup,cosets71.3.2Isomorphism,automorphism,homomorphism81.3.3LiegroupsandLiealgebras91.3.4Representations:faithful,irreducible,reducible,completelyreducible(decomposable),indecomposable,adjoint,fundamental101.3.5RelationbetweenLiealgebrasandLiegroups,Casimiroperators,ran
4、kofagroup111.3.6Schur'slemmas121.3.7SemidirectsumofLiealgebrasandsemidirectproductofLiegroups(inhomogeneousLiealgebrasandgroups)121.3.8TheHaarmeasure131.4Remarkabouttheintroductionofangularmomentum142SymmetryinQuantumMechanics162.1Definitionofsymmetry162.1.1Generalconsiderations16
5、2.1.2Formaldefinitionofsymmetry;raycorrespondence202.2Wigner'stheorem:theexistenceofunitaryoranti-unitaryrepresentations212.3Continuousmatrixgroupsandtheirgenerators282.3.1Generalconsiderations282.3.2Continuousmatrixgroups;decompositionintopieces292.3.3TheLiealgebra(Liering,infini
6、tesimalring)302.3.4Canonicalcoordinates322.3.5Thestructureofthegroupanditsinfinitesimalring362.3.6Summary:continuousmatrixgroupsandtheirLiealgebra382.3.7Grouprepresentations392.4Thephysicalsignificanceofsymmetries42viiviiiCONTENTS2.4.1Continuousgroupsconnectedtotheidentity;Noether
7、'stheorem422.4.2Piecesnotconnectedtotheidentity;discretegroups452.4.3Super-selectionrules452.4.4Completesymmetrygroup,completesetsofcommutingobservables,completesetsofstates492.4.5Summaryofthechapter523RotationsinThree-DimensionalSpace533.1Generalremarksonrotations533.1.1Interpret
8、ation533.1.2Parametersdescribinga
