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书名: | 物理学家用的张量和群论导论 |
作者: | [美]N.杰夫基 |
出版社: | 世界图书出版有限公司 |
出版日期: | 2013-09-01 |
版次: | 1 |
ISBN: | 9787510070266 |
市场价: | 49.0 |
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PartILinearAlgebraandTensorsIAQuicklntroductiontoTensors2VectorSpaces2.1DefinitionandExamples2.2Span,Linearlndependence,andBases2.3Components2.4LinearOperators2.5DuaISpaces2.6Non-degenerateHermitianForms2.7Non-degenerateHermitianFormsandDualSpaces2.8Problems3Tensors3.1DefinitionandExamples3.2ChangeofBasis3.3ActiveandPassiveTransformations3.4TheTensorProduct-DefinitionandProperties3.5TensorProductsofVandV*3.6ApplicationsoftheTensorProductinClassicalPhysics3.7ApplicationsoftheTensorProductinQuantumPhysics3.8SymmetricTensors3.9AntisymmetricTensors3.10ProblemsPartllGroupTheory4Groups,LieGroups,andLieAlgebras4.1Groups-DefinitionandExamples4.2TheGroupsofClassicalandQuantumPhysics4.3Homomorphismandlsomorphism4.4FromLieGroupstoLieAlgebras4.5LieAlgebras-Definition,Properties,andExamples4.6TheLieAlgebrasofClassicalandQuantumPhysics4.7AbstractLieAlgebras4.8HomomorphismandlsomorphismRevisited4.9Problems5BasicRepresentationTheory5.1Representations:DefinitionsandBasicExamples5.2FurtherExamples5.3TensorProduetRepresentations5.4SymmetricandAntisymmetricTensorProductRepresentations5.5EquivalenceofRepresentations5.6DirectSumsandlrreducibility5.7Moreonlrreducibility5.8ThelrreducibleRepresentationsofsu(2),SU(2)andS0(3)5.9ReaIRepresentationsandComplexifications5.10TheIrreducibleRepresentationsofst(2,C)nk,SL(2,C)andS0(3,1)o5.11IrreducibilityandtheRepresentationsof0(3,1)andItsDoubleCovers5.12Problems6TheWigner-EckartTheoremandOtherApplications6.1TensorOperators,SphericalTensorsandRepresentationOperators6.2SelectionRulesandtheWigner-EckartTheorem6.3GammaMatricesandDiracBilinears6.4ProblemsAppendixComplexificationsofRealLieAlgebrasandtheTensorProductDecompositionofsl(2,C)rtRepresentationsA.1DirectSumsandComplexificationsofLieAlgebrasA.2RepresentationsofComplexifiedLieAlgebrasandtheTensorProductDecompositionofst(2,C)RRepresentationsReferencesIndex
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Thiookiscomposedoftwoparts:PartI(Chaps.Ithrough3)isanintroductiontotensorsandtheirphysicalapplications,andPartII(Chaps.4through6)introducesgrouptheoryandintertwinesitwiththeearliermaterial.Bothpartsarewrittenattheadvanced-undergraduate/beginninggraduatelevel,althoughinthecourseof'PartIIthesophisticationlevelrisessomewhat.Thoughthetwopartsdiffersomewhatinflavor,lhaveaimedinbothtofilla(perceived)gapintheliteraiurebyconnecting
thecomponentformalismsprevalentinphysicscalculationstotheabstractbutmoreconceptualformulationsfoundinthemathliterature.Myfirmbeliefisthatweneedtoseetensorsandgroupsincoordinatestogetasenseofhowtheywork,butalsoneedanabstractformulationtounderstandtheiressentialnatureandorganizeourthiaboutthem.
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杰夫基编著的《物理学家用的张量和群论导论》是一部讲述张量和群论的物理学专业的教程,用直观、严谨的方法介绍张量和群论以及其在理论物理和应用数学的重要。本书旨在用一种比较的框架,揭开张量的神秘面纱,使得读者在经典物理和量子物理的背景理解它。将物理计算中的许多流形公式和数学中的抽象的或者更加概念公式的联系起来,对张量和群论的的人来说,这项工作是很欢迎的。
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