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 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, 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; consequently, the book should be of interest also to mathematics students. Ideal for graduate and advanced undergraduate students of physics, engineering and mathematics as a course text or for self study.
Rezensionen / Stimmen
'This book will be useful to graduate and advanced undergraduate students of physics, engineering, and mathematics.' Zentralblatt MATH 'This book provides a highly detailed account of the intricacies involved in considering geometrical concepts.' Contemporary Physics
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Für höhere Schule und Studium
Editions-Typ
Illustrationen
120 Line drawings, unspecified
Maße
Höhe: 262 mm
Breite: 184 mm
Dicke: 42 mm
Gewicht
ISBN-13
978-0-521-83330-1 (9780521833301)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
University of California, San Diego
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 Poincare 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 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.
