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 ...
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.
原文摘录
· · · · · ·
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. (查看原文)
1 有用 糊涂散人 2012-05-27 19:11:19
不适合凝聚态方向的研究者，讲微分流形太多拓扑太少。实际上Nash那本物理几何与拓扑很不错，还有Nakahara的也很好。
1 有用 谦信 2012-05-25 16:37:10
流形与群
0 有用 Sun 2009-03-16 14:46:25
平庸的教材
1 有用 王小七 2012-10-16 00:01:53
如果想领略物理学的美，规范场论和广相是必然的结果，但倘若仅从传统的张量分析进入这两门理论还未能有畅快淋漓的感觉。最好的途径就是直接从微分几何的语言开始。然而此书实为枯燥，各中解释过于啰嗦详细，不适合快速入门，建议仅作为词典之用。推荐《规范场，纽结和引力》一书，实为入门所适用
1 有用 王小七 2012-10-16 00:01:53
如果想领略物理学的美，规范场论和广相是必然的结果，但倘若仅从传统的张量分析进入这两门理论还未能有畅快淋漓的感觉。最好的途径就是直接从微分几何的语言开始。然而此书实为枯燥，各中解释过于啰嗦详细，不适合快速入门，建议仅作为词典之用。推荐《规范场，纽结和引力》一书，实为入门所适用
1 有用 糊涂散人 2012-05-27 19:11:19
不适合凝聚态方向的研究者，讲微分流形太多拓扑太少。实际上Nash那本物理几何与拓扑很不错，还有Nakahara的也很好。
1 有用 谦信 2012-05-25 16:37:10
流形与群
0 有用 Sun 2009-03-16 14:46:25
平庸的教材