物理学家的几何学（第二版）——天元基金影印系列丛书

    This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, elasticity theory, the geometry and topology of Kirchhoff’s electric circuit laws, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers, quarks, and the quark model for mesons. Before a discussion of abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should be of interest also to mathematics students.
This book will be useful to graduate and advanced undergraduate students of physics, engineering, and mathematics. It can be used as a course text of for self-study.
This second edition includes three new appendices, Appendix C, Symmetries, Quarks, and Meson Masses (which concludes with the famous Gell-Mann/Okubo mass formula); Appendix D, Representations and Hyperelastic Bodies; and Appendix E, Orbits and Morse-Bott Theory in Compact Lie Groups. Both Appendix C and D involve results from the theory of representations of compact Lie groups, which are developed here. Appendix E delves deeper into the geometry and topology of compact Lie groups.

Preface to the Second Edition
Perface to the Revised Printing
Perface to the First Edition
Ⅰ Manifolds, Tensors, and Exterior Forms
1 Manifolds and Vector Fields
2 Tensors and Exterior Forms
3 Integration of Differential Forms
4 The Lie Derivative
5 The Poincaré Lemma and Potentials
6 Holonomic and Nonholonomic Constraints
Ⅱ Geometry and Topology
7 R3 and Minkowski Space
8 The Geometry of Surfaces in R3
9 Covariant Differentiation and Curvature
10 Geodesics
11 Relativity, Tensors, and Curvature
12 Curvature and Topology: Synge’s Theorem
13 Betti Numbers and De Rham’s Theorem
14 Harmonic Forms
Ⅲ Lie Groups, Bundles, and Chern Forms
15 Lie Groups
16 Vector Bundles in Geometry and Physics
17 Fiber Bundles, Gauss |Bonnet, and Topological Quantization
18 Connections and Associated Bundles
19 The Dirac Equation
20 Yang |Mills Fields
21 Betti Numbers and Covering Spaces
22 Chern Forms and Homotopy Groups

This second edition differs mainly in the addition of three new appendices: C, D, and E, Appendices C and D are applications of the elements of representation theory of compact Lie groups. Appendix C deals with applications to the flavored quark model that revolutionized particle physics. We illustrate how certain observed mesons (pions, kaons, and etas) are described in terms of quarks and how one can "derive" the mass formula of GellManrdOkubo of 1962. This can be read after Section 20.3b. Appendix D is Concerned with isotropic hy..