Differential Geometry, Gauge Theories, and Gravity

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.

Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.

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.

Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced by digital technology, enabling Cambridge to keep the book in print for specialists and students when other traditional methods of printing would have been infeasible.