物理学家用的张量和群论导论 英文【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

物理学家用的张量和群论导论 英文PDF格式电子书版下载

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Part Ⅰ Linear Algebra and Tensors3

1 A Quick Introduction to Tensors3

2 Vector Spaces9

2.1 Definition and Examples9

2.2 Span,Linear Independence,and Bases14

2.3 Components17

2.4 Linear Operators21

2.5 Dual Spaces25

2.6 Non-degenerate Hermitian Forms27

2.7 Non-degenerate Hermitian Forms and Dual Spaces31

2.8 Problems33

3 Tensors39

3.1 Definition and Examples39

3.2 Change of Basis43

3.3 Active and Passive Transformations49

3.4 The Tensor Product—Definition and Properties53

3.5 Tensor Products of V and V＊55

3.6 Applications of the Tensor Product in Classical Physics58

3.7 Applications of the Tensor Product in Quantum Physics60

3.8 Symmetric Tensors68

3.9 Antisymmetric Tensors70

3.10 Problems81

Part Ⅱ Group Theory87

4 Groups,Lie Groups,and Lie Algebras87

4.1 Groups—Definition and Examples88

4.2 The Groups of Classical and Quantum Physics96

4.3 Homomorphism and Isomorphism103

4.4 From Lie Groups to Lie Algebras111

4.5 Lie Algebras—Definition,Properties,and Examples115

4.6 The Lie Algebras of Classical and Quantum Physics121

4.7 Abstract Lie Algebras127

4.8 Homomorphism and Isomorphism Revisited131

4.9 Problems138

5 Basic Representation Theory145

5.1 Representations：Definitions and Basic Examples145

5.2 Further Examples150

5.3 Tensor Product Representations159

5.4 Symmetric and Antisymmetric Tensor Product Representations165

5.5 Equivalence of Representations169

5.6 Direct Sums and Irreducibility177

5.7 More on Irreducibility184

5.8 The Irreducible Representations of su(2),SU(2)and SO(3)188

5.9 Real Representations and Complexifications193

5.10 The Irreducible Representations of sl(2,C)R,SL(2,C)and SO(3,1)o196

5.11 Irreducibility and the Representations of O(3,1)and Its Double Covers204

5.12 Problems208

6 The Wigner-Eckart Theorem andO ther Applications213

6.1 Tensor Operators,Spherical Tensors and Representation Operators213

6.2 Selection Rules and the Wigner-Eckart Theorem217

6.3 Gamma Matrices and Dirac Bilinears222

6.4 Problems225

Appendix Complexifications of Real Lie Algebras and the Tensor Product Decomposition of sl(2,C)R Representations227

A.1 Direct Sums and Complexifications of Lie Algebras227

A.2 Representations of Complexified Lie Algebras and the Tensor Product Decomposition of sl(2,C)R Representations229

References235

Index237