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性。本书旨在用一种比较独特的框架，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性公式的联系起来，对张量和群论的的人来说，这项工作是很欢迎的。

Part Ⅰ Linear Algebra and Tensors

 1 A Quick Introduction to Tensors

 2 Vector Spaces

2.1 Definition and Examples

2.2 Span, Linear Independence, and Bases

2.3 Components

2.4 Linear Operators

2.5 Dual Spaces

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 Change of Basis

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 of the 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

Part Ⅱ Group Theory

 4 Groups, Lie Groups, and Lie Algebras

4.1 Groups--Definition and Examples

4.2 The Groups of Classical and Quantum Physics

4.3 Homomorphism and Isomorphism

4.4 From Lie Groups to Lie Algebras

4.5 Lie Algebras--Definition, Properties, and Examples

4.6 The Lie Algebras of Classical and Quantum Physics

4.7 Abstract Lie Algebras

4.8 Homomorphism and Isomorphism Revisited

4.9 Problems

 5 Basic Representation Theory

5.1 Representations: Definitions and Basic Examples

5.2 Further Examples

5.3 Tensor Product Representations

5.4 Symmetric and Antisymmetric Tensor Product Representations

5.5 Equivalence of Representations

5.6 Direct Sums and Irreducibility

5.7 More on Irreducibility

5.8 The Irreducible Representations of su(2), SU(2) and SO(3)

5.9 Real Representations and Complexifications

5.10 The Irreducible Representations of sl(2, C)R, SL(2, C) andS0(3, 1)o

5.11 Irreducibility and the Representations of O(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 of sl(2, C)R Representations

 A.1 Direct Sums and Complexifications of Lie Algebras

 A.2 Representations of Complexified Lie Algebras and the Tensor Product Decomposition of s[(2, C)R Representations

References

Index