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211020 ||| eng |
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|a 9781139061377
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| 050 |
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4 |
|a QC20.7.D52
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| 100 |
1 |
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|a Frankel, Theodore
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| 245 |
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|a The geometry of physics
|b an introduction
|c Theodore Frankel
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| 250 |
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|a 3rd ed
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| 260 |
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|a Cambridge
|b Cambridge University Press
|c 2012
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| 300 |
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|a lxii, 686 pages
|b digital
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| 505 |
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|a Overview: an informal overview of Cartan's exterior differential forms, illustrated with an application to Cauchy's stress tensor -- t I. Part I: Manifolds and vector fields -- Tensors and exterior forms -- Integration of differential forms -- The Lie derivative -- The Poincare Lemma and potentials -- Holonomic and nonholonomic constraints --Part II: Geometry and topology -- R3 and Minkowski space -- The geometry of surfaces in R3 -- Covariant differentiation and curvature -- Geodesics -- Relativity, tensors, and curvature -- Curvature and topology: Synge's theorem -- Betti numbers and De Rham's theorem -- Harmonic forms -- Part III: Lie Groups -- Vector bundles in geometry and physics -- Fiber bundles, Gauss-Bonnet, and topological quantization -- Connections and associated bundles -- The Dirac equation -- Yang-Mills fields -- Betti numbers and covering spaces -- Chern forms and homotopy groups
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| 653 |
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|a Geometry, Differential
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| 653 |
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|a Mathematical physics
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b CBO
|a Cambridge Books Online
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| 028 |
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|a 10.1017/CBO9781139061377
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| 856 |
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|u https://doi.org/10.1017/CBO9781139061377
|x Verlag
|3 Volltext
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| 082 |
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|a 530.15636
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| 520 |
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|a This book provides 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, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text
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