Differential Geometry, Gauge Theories, and Gravity [Paperback]

Emphasizing the applications of differential geometry to gauge theories in particle physics and general relativity, this work will be of special interest for researchers in applied mathematics or theoretical physics.Emphasizing the applications of differential geometry to gauge theories in particle physics and general relativity, this work will be of special interest for researchers in applied mathematics or theoretical physics.Using a self-contained and concise treatment of modern differential geometry, this book will be of great interest to graduate students and researchers in applied mathematics or theoretical physics working in field theory, particle physics, or general relativity. The authors begin with an elementary presentation of differential forms. This formalism is then used to discuss physical examples, followed by a generalization of the mathematics and physics presented to manifolds. The book emphasizes the applications of differential geometry concerned with gauge theories in particle physics and general relativity. Topics discussed include Yang-Mills theories, gravity, fiber bundles, monopoles, instantons, spinors, and anomalies.Preface; 1. Exterior algebra; 2. Differential forms on open subsets of Rn; 3. Metric structures; 4. Gauge theories; 5. EinsteinCartan theory; 6. The Lie derivative; 7. Manifolds; 8. Lie groups; 9. Fibre bundles; 10. Monopoles, instantons, and related fibre bundles; 11. Spin; 12. An algebraic approach to anomalies; 13. Anomalies from graphs; References; Bibliography; Notation; Index. ...a very beautifully and elegantly written introduction to those areas of modern differential geometry that either now play, or presumably will play, a role in particle physics and general relativity. SIAM Review