Research Catalog

Title

The geometry of physics : an introduction / Theodore Frankel.

Author

Frankel, Theodore, 1929-2017.

Publication

New York : Cambridge University Press, 2004.

Items in the Library & Off-site

Details

Description

xxvi, 694 p. : ill.; 26 cm.

Summary

"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 to both classical and modern physics and engineering. 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 or for self-study."--Jacket.

Subjects

• Differential topology
• Algebraic topology
• Geometry, Differential
• Mathematical physics

Bibliography (note)

• Includes bibliographical references (p. 679-681) and index.

Contents

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 -- 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 -- 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.

ISBN

• 0521833302
• 9780521833301
• 0521539277
• 9780521539272

LCCN

2003044030

OCLC

• ocm51855212
• 51855212
• SCSB-1320893

Owning Institutions

Princeton University Library