The Geometry of Physics
Cambridge University Press (Verlag)
978-0-521-38753-8 (ISBN)
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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, thermodynamics, the deformation tensors of elasticity, 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. Before discussing 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 also be of interest 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 or for self study.
Preface; Part 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 non-holonomic constraints; Part 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; Part III. Lie Groups, Bundles and Chern Forms: 15. Lie groups; 16. Vector bundles in geometry and physics; 17. Fiber bundles, Gauss–Bonnet, 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; Appendix: forms in continuum mechanics.
| Erscheint lt. Verlag | 13.4.1999 |
|---|---|
| Zusatzinfo | 120 Line drawings, unspecified |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 179 x 255 mm |
| Gewicht | 1155 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 0-521-38753-1 / 0521387531 |
| ISBN-13 | 978-0-521-38753-8 / 9780521387538 |
| Zustand | Neuware |
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