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Overview
Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations. Topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory. "Thoroughly recommended." — Physics Bulletin. 1983 edition.Synopsis
This volume provides an easily comprehensible introduction to topological and geometrical methods in theoretical physics and applied mathematics. No detailed knowledge of topology or geometry is required in the reader, and advanced undergraduate or graduate physicists should have no difficulty in understanding the material.
The style and approach of the book reflect the fact that the authors are themselves physicists, and have taken trouble to clarify difficult mathematical concepts and to emphasize their physical motivation. The applications range from condensed matter physics and statistical mechanics to elementary particle theory, while the main mathematical topics are differential forms, homotopy, homology, cohomology, fibre bundles, connection and covariant derivatives and Morse theory.