物理学家用的张量和群论导论

书籍目录

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

partii 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

作者简介

这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。《物理学家用的张量和群论导论》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。物理和应用数学专业的高年级本科生和研究生都将受益于本书。

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