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part i linear algebra and tensors
i a quicklntroduction to tensors
2 vectorspaces
2.1 definition and examples
2.2 span,linearlndependence,and bases
2.3 components
2.4 linearoperators
2.5 duaispaces
2.6 non-degenerate hermitian forms
2.7 non-degenerate hermitian forms and dual spaces
2.8 problems
3 tensors
3.1 definition and examples
3.2 changeofbasis
3.3 active and passive transformations
3.4 the tensor product-definition and properties
3.5 tensor products of v and v*
3.6 applications ofthe tensor product in classical physics
3.7 applications of the tensor product in quantum physics
3.8 symmetric tensors
3.9 antisymmetric tensors
3.10 problems

partll grouptheory
4 groups, lie groups,and lie algebras
4.1 groups-definition and examples
4.2 the groups ofclassical and quantum physics
4.3 homomorphismandlsomorphism
4.4 from lie groups to lie algebras
4.5 lie algebras-definition,properties,and examples
4.6 the lie algebras ofclassical and quantum physics
4.7 abstractliealgebras
4.8 homomorphism andlsomorphism revisited
4.9 problems
5 basic representation theory
5.1 representations: definitions and basic examples
5.2 furtherexamples
5.3 tensorproduet representations
5.4 symmetric and antisymmetric tensor product representations
5.5 equivalence ofrepresentations 
5.6 direct sums andlrreducibility
5.7 moreonlrreducibility
5.8 thelrreducible representations ofsu£¨2£©,su£¨2£© and s0£¨3£©
5.9 reairepresentations andcomplexifications
5.10 the irreducible representations of st£¨2, c£©nk, sl£¨2, c£© ands0£¨3,1£©o
5.11 irreducibility and the representations of 0£¨3, 1£© and its double covers
5.12 problems
6 the wigner-eckart theorem and other applications
6.1 tensor operators, spherical tensors and representation operators
6.2 selection rules and the wigner-eckart theorem
6.3 gamma matrices and dirac bilinears
6.4 problems
appendix  complexifications of real lie algebras and the tensor
product decomposition ofsl£¨2,c£©rt representations
a.1 direct sums and complexifications oflie algebras
a.2 representations of complexified lie algebras and the tensor
product decomposition ofst£¨2,c£©r representations
references
index