Differential Geometry, Gauge Theories and Gravity

ISBN-13: 9780521378215 / Angielski / Miękka / 1989 / 244 str.

M. Gockeler; T. Schucker

Opis

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.

Recenzje

"...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

Spis treści

Preface; 1. Exterior algebra; 2. Differential forms on open subsets of Rn; 3. Metric structures; 4. Gauge theories; 5. Einstein–Cartan 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.