《物理學家的幾何學》是2005年清華大學出版社出版的圖書，作者是[美]Theodore Frankel。
基本介紹
- 中文名：物理學家的幾何學
- 外文名：The Geometry of Physics An Introduction 2nd ed.
- 作者：[美]Theodore Frankel
- 出版社：清華大學出版社
- 出版日期：2005-3-1
圖書信息,圖書簡介,目錄,
圖書信息
書名：The Geometry of Physics An Introduction 2nd ed.（物理學家的幾何學 第2版）
ISBN：9787302073512
作者：[美]Theodore Frankel
定價：84元
出版日期：2005-3-1
出版社：清華大學出版社
圖書簡介
本書試圖提供外微分形式、微分幾何、代數拓撲、微分拓撲、李群、向量叢、Chern公式等前沿知識，它們對於深入理解經典物理、現代物理以及工程都是必需的。其中包含解析動力學、流體動力學、電磁學（在平坦空間和彎曲空間）、熱力學、彈性理論、Kirchhoff電路定律的幾何及拓撲、肥皂泡薄膜、狹義相對論和廣義相對論、Dirac運算元和旋量、Yang-Mills規範場、Aharonov-Bohm效應、Berry相、瞬子繞數、夸克、介子的夸克模型。在討論抽象的微分幾何概念前，通過大量的關於常規空間中曲面的研究培養幾何直觀，因此，學數學的學生對此書也會很感興趣。
本書對於物理、工程、數學的高年級學生和研究生是非常有益的，可供他們作為自學教材。
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.
目錄
本書試圖提供外微分形式、微分幾何、代數拓撲、微分拓撲、李群、向量叢、Chern公式等前沿知識，它們對於深入理解經典物理、現代物理以及工程都是必需的。其中包含解析動力學、流體動力學、電磁學（在平坦空間和彎曲空間）、熱力學、彈性理論、Kirchhoff電路定律的幾何及拓撲、肥皂泡薄膜、狹義相對論和廣義相對論、Dirac運算元和旋量、Yang-Mills規範場、Aharonov-Bohm效應、Berry相、瞬子繞數、夸克、介子的夸克模型。在討論抽象的微分幾何概念前，通過大量的關於常規空間中曲面的研究培養幾何直觀，因此，學數學的學生對此書也會很感興趣。
本書對於物理、工程、數學的高年級學生和研究生是非常有益的，可供他們作為自學教材。
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.
