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1、SymmetriesinQuantumPhysicsThisPageIntentionallyLeftBlankSymmetriesinQuantumPhysicsU.FanoDepartmentofPhysicsandJamesFranckInstituteUniversityofChicagoChicago,IllinoisA.R.P.RauDepartmentofPhysicsandAstronomyLouisianaStateUniversityBatonRouge,LouisianaAcademicPressSanDiegoNewYorkBostonLondo
2、nSydneyTokyoTorontoThisbookisprintedonacid-fleepaper.(~Copyright91996byACADEMICPRESS,INC.AllRightsReserved.Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical,includingphotocopy,recording,oranyinformationstorageandretrievalsystem,withoutpermis
3、sioninwritingfromthepublisher.AcademicPress,Inc.ADivisionofHarcourtBrace&Company525BStreet,Suite1900,SanDiego,California92101-4495UnitedKingdomEditionpublishedbyAcademicPressLimited24-28OvalRoad,LondonNW17DXLibraryofCongressCataloging-in-PublicationDataFano,Ugo.Symmetriesinquantumphysics
4、/editedbyU.Fano,A.R.P.Rau.p.cm.Includesindex.ISBN0-12-248455-X(alk.paper)1.Quantumtheory--Mathematics.2.Symmetry(Physics)--Methodology.3.Mathematicalphysics.I.Fano,Ugo.II.Rau,A.R.P.(A.RaviP.)QC174.17.M35S961996530.1'2--dc2096-2004CIPPRINTEDINTHEUNITEDSTATESOFAMERICA969798990001BC98765432
5、1ContentsPrefacexiii1Introduction1TransformationTheories:Klein'sandDirac's........31.1SymmetryandtheSelectionofVariables...........51.1.1Examplesoftensorialequations............51.2AlgebraicElements.......................111.2.1Vectors,tensors,andrelatedquantities........111.2.2Additiona
6、nddirectproductoftensorialsets....141.2.3Lineartransformation.................141.3ReductionProcedureandIrreducibleTensorialSets.....171.3.1Ananalyticalexample:Reductionoftensors....181.4FurtherAspectsofReduction.................201.4.1Reductionprocedures.................211.4.2Labelingo
7、fsetelements................221.4.3Blockdiagonalizationofthereduction........231.4.4Phasenormalization..................231.4.5Grouptheory......................241.4.6Reductionasanexpansionintoeigenfunctions...251.5StructureoftheBook.....................261.5.1Alternative
