Göckeler M., Schücker T. Differential Geometry, Gauge Theories, and Gravity

Cambridge University Press, 1989. — 244 p. — (Cambridge Monographs on Mathematical Physics). — ISBN: 9780521378215.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.Exterior algebra
Differential forms on open subsets of Rn
Metric structures
Gauge theories
Einstein–Cartan theory
The Lie derivative
Manifolds
Lie groups
Fibre bundles
Monopoles, instantons, and related fibre bundles
Spin
An algebraic approach to anomalies
Anomalies from graphs