物理学家用的张量和群论导论

Definitions and Basic Examples5.2 FurtherExamples5.3 TensorProduet Representations5.4 Symmetric and Antisymmetric Tensor Product Representations5.5 Equivalence ofRepresentations 5.6 Direct Sums andlrreducibility5.7 Moreonlrreducibility5.8 Thelrreducible Representations ofsu（2）,SU（2） and S0（3）5.9 ReaIRepresentations andComplexifications5.10 The Irreducible Representations of st（2, C）nk, SL（2, C） andS0（3,1）o5.11 Irreducibility and the Representations of 0（3, 1） and Its Double Covers5.12 Problems6 The Wigner-Eckart Theorem and Other Applications6.1 Tensor Operators, Spherical Tensors and Representation Operators6.2 Selection Rules and the Wigner-Eckart Theorem6.3 Gamma Matrices and Dirac Bilinears6.4 ProblemsAppendix Complexifications of Real Lie Algebras and the TensorProduct Decomposition ofsl（2,C）rt RepresentationsA.1 Direct Sums and Complexifications ofLie AlgebrasA.2 Representations of Complexified Lie Algebras and the TensorProduct Decomposition ofst（2,C）R RepresentationsReferencesIndex

This book is composed of two parts Part I （Chaps. I through 3） is an introduction to tensors and their physical applications， and Part II （Chaps. 4 through 6） introduces group theory and intertwines it with the earlier material. Both parts are written at the advanced-undergraduate/beginning graduate level， although in the course of' Part II the sophistication level rises somewhat. Though the two parts differ somewhat in flavor，l have aimed in both to fill a （perceived） gap in the literaiure by connecting　　the component formalisms prevalent in physics calculations to the abstract but more conceptual formulations found in the math literature. My firm beliefis that we need to see tensors and groups in coordinates to get a sense of how they work， but also need an abstract formulation to understand their essential nature and organize our thinking about them.