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