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.
具體描述
讀後感
这本书最伟大的价值从第三部分开始展现. 非常有趣. 值得花时间啃. 当然,要研读这有趣的部分,微分几何的基础是要稍微有了解的,这就是此书的第一部分和第二部分的主要内容了.
評分这本书最伟大的价值从第三部分开始展现. 非常有趣. 值得花时间啃. 当然,要研读这有趣的部分,微分几何的基础是要稍微有了解的,这就是此书的第一部分和第二部分的主要内容了.
評分这本书最伟大的价值从第三部分开始展现. 非常有趣. 值得花时间啃. 当然,要研读这有趣的部分,微分几何的基础是要稍微有了解的,这就是此书的第一部分和第二部分的主要内容了.
評分这本书最伟大的价值从第三部分开始展现. 非常有趣. 值得花时间啃. 当然,要研读这有趣的部分,微分几何的基础是要稍微有了解的,这就是此书的第一部分和第二部分的主要内容了.
評分这本书最伟大的价值从第三部分开始展现. 非常有趣. 值得花时间啃. 当然,要研读这有趣的部分,微分几何的基础是要稍微有了解的,这就是此书的第一部分和第二部分的主要内容了.
用戶評價
不適閤凝聚態方嚮的研究者，講微分流形太多拓撲太少。實際上Nash那本物理幾何與拓撲很不錯，還有Nakahara的也很好。
评分不適閤凝聚態方嚮的研究者，講微分流形太多拓撲太少。實際上Nash那本物理幾何與拓撲很不錯，還有Nakahara的也很好。
评分流形與群
评分如果想領略物理學的美，規範場論和廣相是必然的結果，但倘若僅從傳統的張量分析進入這兩門理論還未能有暢快淋灕的感覺。最好的途徑就是直接從微分幾何的語言開始。然而此書實為枯燥，各中解釋過於囉嗦詳細，不適閤快速入門，建議僅作為詞典之用。推薦《規範場，紐結和引力》一書，實為入門所適用
评分不適閤凝聚態方嚮的研究者，講微分流形太多拓撲太少。實際上Nash那本物理幾何與拓撲很不錯，還有Nakahara的也很好。
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