• 物理学家用的张量和群论导论
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物理学家用的张量和群论导论

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北京东城
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作者[美]杰夫基(Jeevanjee N.) 著

出版社世界图书出版公司

出版时间2014-03

版次1

装帧平装

货号A5

上书时间2024-12-24

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图书标准信息
  • 作者 [美]杰夫基(Jeevanjee N.) 著
  • 出版社 世界图书出版公司
  • 出版时间 2014-03
  • 版次 1
  • ISBN 9787510070266
  • 定价 49.00元
  • 装帧 平装
  • 开本 24开
  • 纸张 胶版纸
  • 页数 242页
  • 正文语种 英语
【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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