The Geometry of Physics
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Beschreibung'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.Theodore Frankel explains 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. It can be used as a course text or for self study.
InhaltsverzeichnisPreface to the Third Edition; Preface to the Second Edition; Preface to the revised printing; Preface to the First Edition; Overview; 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 Poincare Lemma and potentials; 6. Holonomic and nonholonomic 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 A. Forms in continuum mechanics; Appendix B. Harmonic chains and Kirchhoff's circuit laws; Appendix C. Symmetries, quarks, and Meson masses; Appendix D. Representations and hyperelastic bodies; Appendix E. Orbits and Morse-Bott theory in compact Lie groups.
PortraitTheodore Frankel received his PhD from the University of California, Berkeley. He is currently Emeritus Professor of Mathematics at the University of California, San Diego.
PressestimmenReviews of previous editions: '... highly readable and enjoyable ... The book will make an excellent course text or self-study manual for this interesting subject.' Physics Today 'This book provides a highly detailed account of the intricacies involved in considering geometrical concepts.' Contemporary Physics 'If you're looking for a well-written and well-motivated introduction to differential geometry, this one looks hard to beat.' Fernando Q. Gouvea, MAA Online '... a first rate introductory textbook ... the style is lively and exposition is clear which make the text easy to read ... This book will be beneficial to students and scientists wishing to learn the foundations of differential geometry and algebraic topology as well as geometric formulations of modern physical theories.' Pure and Applied Geophysics '... this book should not be missing in any physics or mathematics library.' European Mathematical Society 'This book is a great read and has a lot to offer to graduate students in both mathematics and physics. I wish I had had it on my desk when I began studying geometry.' AMS Review 'The layout, the typography and the illustrations of this advanced textbook on modern mathematical methods are all very impressive and so are the topics covered in the text.' Zentralblatt fur Mathematik und ihre Grenzgebiete
Untertitel: An Introduction. 3rd edition. 260 b/w illus. 205 exercises. Sprache: Englisch.
Verlag: Cambridge University Pr.
Erscheinungsdatum: November 2011
Seitenanzahl: 748 Seiten