物理学家用的张量和群论导论

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