群論和物理學(英文)（簡體書）

Group theory is one of the great achievements of 19th century mathematics. It emerged as a unifying idea drawing on four different sources: number theory, the theory of equations, geometry, and crystallography. The early motivation from number theory stemmed from the work of Euler, Legendre and Gauss on power residues. In the theory of equations, the study of various permutation groups became increasingly important through the work of Lagrange, Ruffini, Gauss, Abel, Cauchy, and especially Galois. The discovery of new types of geometries-including non-Euclidean, affine, projective etc.-led, eventually, to the famous Erlangen program of Klein, which proposed that the true study of any geometry lies in an analysis of its group of motions. In crystallography, the possible symmetries of the internal structure of a crystal were enumerated long before there was any possibility of its physical d本書是根據作者在哈佛大學的授課講義編寫而成的，詳細介紹了群論及其在物理學中的應用。書中還論及許多現代課題，對SU（n）群及表示也作了大篇幅論述。本書的特點是將物理學與數學溶為一體，闡述數學理論時顧及物理應用。
目次：基本定義和例子；有限群表示理論；分子振動和齊次向量叢；緊致群和李群；SU（n）的不可約表示。附錄7則。
讀者對象：物理專業的研究人員和大學師生、研究生，理論物理工作者。

Preface
1 Basic definitions and examples
　1.1 Groups: definition and examples
　1.2 Homomorphisms: the relation between SL 2, and the Lorentz group
　1.3 The action of a group on a set
　1.4 Conjugation and conjugacy classes
　1.5 Applications to crystallography
　1.6 The topology of SU 2 and SO 3
　1.7 Morphisms
　1.8 The classification of the finite subgroups of SO 3
　1.9 The classification of the finite subgroups of O 3
　1.10 The icosahedral group and the fullerenes
2 Representation theory of finite groups
　2.1 Definitions, examples, irreducibility
　2.2 Complete reducibility
　2.3 Schurs lemma
　2.4 Characters and their orthogonality relations
　2.5 Action on function spaces
　2.6 The regular representation
　2.7 Character tables
　2.8 The representations of the symmetric group
3 Molecular vibrations and homogeneous vector bundles
　3.1 Small oscillations and group theory
　3.2 Molecular displacements and vector bundles
　3.3 Induced representations
　3.4 Principal bundles
　3.5 Tensor products
　3.6 Representative operators and quantum mechanical selection rules
　3.7 The semiclassical theory of radiation
　3.8 Semidirect products and their representations
　3.9 Wigners classification of the irreducible representations of the Poincare group
　3.10 Parity
　3.11 The Mackey theorems on induced representations, with applications to the symmetric group
　3.12 Exchange forces and induced representations
4 Compact groups and Lie groups
　4.1 Haar measure
　4.2 The Peter-Weyl theorem
　4.3 The irreducible representations of SU 2
　4.4 The irreducible representations of SO 3 and spherical harmonics
　4.5 The hydrogen atom
　4.6 The periodic table
　4.7 The shell model of the nucleus
　4.8 The Clebsch-Gordan coefficients and isospin
　4.9 Relativistic wave equations
　4.10 Lie algebras
　4.11 Representations of su 2
5 The irreducible representations of SU n
　5.1 The representation of Gl V on the r-fold tensor product
　5.2 Gl V spans Hornsr TrV, TrV
　5.3 Decomposition of TrV into irreducibles
　5.4 Computational rules
　5.5 Description of tensors belonging to W
　5.6 Representations of Gl V and Sl V on U
　5.7 Weight vectors
　5.8 Determination of the irreducible finite-dimensional repre-sentations of Sl d, C
　5.9 Strangeness
　5.10 The eight-fold way
　5.11 Quarks
　5.12 Color and beyond
　5.13 Where do we stand
Appendix A The Bravais lattices and the arithmetical crystal classes
　A.1 The lattice basis and the primitive cell
　A.2 The 14 Bravais lattices
Appendix B Tensor product
Appendix C Integral geometry and the representations of the symmetric group
　C.1 Partition pairs
　C.2 Proof of the main combinatorial lemma
　C.3 The Littlewood-Richardson rule and Youngs rule
　C.4 The ring of virtual representations of all the Sn
　C.5 Dimension formulas
　C.6 The Murnaghan-Nakayama rule
　C.7 Characters of Gl V
AppendixD Wigners theorem on quantum mechanical symmetries
Appendix E Compact groups, Haar measure, and the Peter-Weyl theorem
Appendix F A history of 19th century spectroscopy
Appendix G Characters and fixed point formulas for Lie groups
Further reading
Index