Differential Geometry, Gauge Theories, and Gravity

by M. Göckeler, T. Schücker

Overview

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.

Product Details

ISBN-13:	9780521378215
Publisher:	Cambridge University Press
Publication date:	07/28/1989
Series:	Cambridge Monographs on Mathematical Physics
Edition description:	Reprint
Pages:	244
Product dimensions:	6.02(w) x 9.06(h) x 0.71(d)

Table of Contents

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.

Editorial Reviews

"...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

From the Publisher