物理学家的几何学 [美]弗兰克尔 清华大学出版社【正版保证】 fb2 免费 lrf 下载 kindle azw3 pdf 阿里云

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， electromagism （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 pact Lie groups， which are developed here。 Appendix E delves deeper into the geometry and topology of pact 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|Bon, 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

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This book is intended primarily for two audiences, first, the physics or engineering student, and second, the mathematics student. My classes in the past have been populated mostly by first-, second-, and third-year graduate students in physics, but there have also been mathematics students and undergraduates. The only real mathematical prerequisites are basic linear algebra and some familiarity with calculus of several variables. Most students (in the United States) have these by the beginning of the third undergraduate year.

书籍介绍

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.