Geometrodynamics of Gauge Fields on the Geometry of Yang-Mills and Gravitational Gauge Theories

E.W. Mielke Geometrodynamics of Gauge Fields On the Geometry of Yang-Mills and Gravitational Gauge Theories

Series: Mathematical Physics Studies

▶ A comprehensive revision of a classic text relating geometic field theory to modern physics ▶ Offers an up-to-date overview of geometrodynamics including minimal topological models ▶ Contains new chapters on teleparalelism, Chern-Simons-induced topological 3D gravity and supergravity, quantization via topological ghosts, constrained BF model with SL (5, R) gauge group, and chiral and trace anomalies ▶ Provides a detailed exposition of frame bundles in gravity

2nd ed. 2017, XVII, 373 p. 18 illus., 8 illus. in This monograph aims to provide a unified, geometrical foundation of gauge theories color. of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions Printed book and topological invariants are included. By transferring these concepts to local space- time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann- Hardcover Cartan space with curvature and torsion. It provides the framework in which the (broken) ISBN 978-3-319-29732-3 Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and ▶ 119,99 € | £109.99 higher-dimensional, non-abelian Kaluza-Klein theories are developed. ▶ *128,39 € (D) | 131,99 € (A) | CHF 141.50

Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.

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