物理学家用的张量和群论导论

物理学家用的张量和群论导论
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作者: [美] (Jeevanjee N.)
2014-03
版次: 1
ISBN: 9787510070266
定价: 49.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 242页
正文语种: 英语
分类: 自然科学
59人买过
  •   Thisbookiscomposedoftwoparts:PartI(Chaps.Ithrough3)isanintroductiontotensorsandtheirphysicalapplications,andPartII(Chaps.4through6)introducesgrouptheoryandintertwinesitwiththeearliermaterial.Bothpartsarewrittenattheadvanced-undergraduate/beginninggraduatelevel,althoughinthecourseof'PartIIthesophisticationlevelrisessomewhat.Thoughthetwopartsdiffersomewhatinflavor,lhaveaimedinbothtofilla(perceived)gapintheliteraiurebyconnecting
      thecomponentformalismsprevalentinphysicscalculationstotheabstractbutmoreconceptualformulationsfoundinthemathliterature.Myfirmbeliefisthatweneedtoseetensorsandgroupsincoordinatestogetasenseofhowtheywork,butalsoneedanabstractformulationtounderstandtheiressentialnatureandorganizeourthinkingaboutthem. PartILinearAlgebraandTensors
    IAQuicklntroductiontoTensors
    2VectorSpaces
    2.1DefinitionandExamples
    2.2Span,Linearlndependence,andBases
    2.3Components
    2.4LinearOperators
    2.5DuaISpaces
    2.6Non-degenerateHermitianForms
    2.7Non-degenerateHermitianFormsandDualSpaces
    2.8Problems
    3Tensors
    3.1DefinitionandExamples
    3.2ChangeofBasis
    3.3ActiveandPassiveTransformations
    3.4TheTensorProduct-DefinitionandProperties
    3.5TensorProductsofVandV*
    3.6ApplicationsoftheTensorProductinClassicalPhysics
    3.7ApplicationsoftheTensorProductinQuantumPhysics
    3.8SymmetricTensors
    3.9AntisymmetricTensors
    3.10Problems

    PartllGroupTheory
    4Groups,LieGroups,andLieAlgebras
    4.1Groups-DefinitionandExamples
    4.2TheGroupsofClassicalandQuantumPhysics
    4.3Homomorphismandlsomorphism
    4.4FromLieGroupstoLieAlgebras
    4.5LieAlgebras-Definition,Properties,andExamples
    4.6TheLieAlgebrasofClassicalandQuantumPhysics
    4.7AbstractLieAlgebras
    4.8HomomorphismandlsomorphismRevisited
    4.9Problems
    5BasicRepresentationTheory
    5.1Representations:DefinitionsandBasicExamples
    5.2FurtherExamples
    5.3TensorProduetRepresentations
    5.4SymmetricandAntisymmetricTensorProductRepresentations
    5.5EquivalenceofRepresentations
    5.6DirectSumsandlrreducibility
    5.7Moreonlrreducibility
    5.8ThelrreducibleRepresentationsofsu(2),SU(2)andS0(3)
    5.9ReaIRepresentationsandComplexifications
    5.10TheIrreducibleRepresentationsofst(2,C)nk,SL(2,C)andS0(3,1)o
    5.11IrreducibilityandtheRepresentationsof0(3,1)andItsDoubleCovers
    5.12Problems
    6TheWigner-EckartTheoremandOtherApplications
    6.1TensorOperators,SphericalTensorsandRepresentationOperators
    6.2SelectionRulesandtheWigner-EckartTheorem
    6.3GammaMatricesandDiracBilinears
    6.4Problems
    AppendixComplexificationsofRealLieAlgebrasandtheTensor
    ProductDecompositionofsl(2,C)rtRepresentations
    A.1DirectSumsandComplexificationsofLieAlgebras
    A.2RepresentationsofComplexifiedLieAlgebrasandtheTensor
    ProductDecompositionofst(2,C)RRepresentations
    References
    Index
  • 内容简介:
      Thisbookiscomposedoftwoparts:PartI(Chaps.Ithrough3)isanintroductiontotensorsandtheirphysicalapplications,andPartII(Chaps.4through6)introducesgrouptheoryandintertwinesitwiththeearliermaterial.Bothpartsarewrittenattheadvanced-undergraduate/beginninggraduatelevel,althoughinthecourseof'PartIIthesophisticationlevelrisessomewhat.Thoughthetwopartsdiffersomewhatinflavor,lhaveaimedinbothtofilla(perceived)gapintheliteraiurebyconnecting
      thecomponentformalismsprevalentinphysicscalculationstotheabstractbutmoreconceptualformulationsfoundinthemathliterature.Myfirmbeliefisthatweneedtoseetensorsandgroupsincoordinatestogetasenseofhowtheywork,butalsoneedanabstractformulationtounderstandtheiressentialnatureandorganizeourthinkingaboutthem.
  • 目录:
    PartILinearAlgebraandTensors
    IAQuicklntroductiontoTensors
    2VectorSpaces
    2.1DefinitionandExamples
    2.2Span,Linearlndependence,andBases
    2.3Components
    2.4LinearOperators
    2.5DuaISpaces
    2.6Non-degenerateHermitianForms
    2.7Non-degenerateHermitianFormsandDualSpaces
    2.8Problems
    3Tensors
    3.1DefinitionandExamples
    3.2ChangeofBasis
    3.3ActiveandPassiveTransformations
    3.4TheTensorProduct-DefinitionandProperties
    3.5TensorProductsofVandV*
    3.6ApplicationsoftheTensorProductinClassicalPhysics
    3.7ApplicationsoftheTensorProductinQuantumPhysics
    3.8SymmetricTensors
    3.9AntisymmetricTensors
    3.10Problems

    PartllGroupTheory
    4Groups,LieGroups,andLieAlgebras
    4.1Groups-DefinitionandExamples
    4.2TheGroupsofClassicalandQuantumPhysics
    4.3Homomorphismandlsomorphism
    4.4FromLieGroupstoLieAlgebras
    4.5LieAlgebras-Definition,Properties,andExamples
    4.6TheLieAlgebrasofClassicalandQuantumPhysics
    4.7AbstractLieAlgebras
    4.8HomomorphismandlsomorphismRevisited
    4.9Problems
    5BasicRepresentationTheory
    5.1Representations:DefinitionsandBasicExamples
    5.2FurtherExamples
    5.3TensorProduetRepresentations
    5.4SymmetricandAntisymmetricTensorProductRepresentations
    5.5EquivalenceofRepresentations
    5.6DirectSumsandlrreducibility
    5.7Moreonlrreducibility
    5.8ThelrreducibleRepresentationsofsu(2),SU(2)andS0(3)
    5.9ReaIRepresentationsandComplexifications
    5.10TheIrreducibleRepresentationsofst(2,C)nk,SL(2,C)andS0(3,1)o
    5.11IrreducibilityandtheRepresentationsof0(3,1)andItsDoubleCovers
    5.12Problems
    6TheWigner-EckartTheoremandOtherApplications
    6.1TensorOperators,SphericalTensorsandRepresentationOperators
    6.2SelectionRulesandtheWigner-EckartTheorem
    6.3GammaMatricesandDiracBilinears
    6.4Problems
    AppendixComplexificationsofRealLieAlgebrasandtheTensor
    ProductDecompositionofsl(2,C)rtRepresentations
    A.1DirectSumsandComplexificationsofLieAlgebras
    A.2RepresentationsofComplexifiedLieAlgebrasandtheTensor
    ProductDecompositionofst(2,C)RRepresentations
    References
    Index
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