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

Springer International Publishing, 2017 — 2nd Ed. — 373p. — (Mathematical Physics Studies) — ISBN: 978-3-319-29734-7 (eBook), 978-3-319-29732-3 (Hardcover).This monograph aims to provide a unified, geometrical foundation of gauge theories 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 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-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed.
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.Historical Background
Geometry of Gauge Fields
Maxwell and Yang–Mills Theory
Gravitation as a Gauge Theory
Einstein–Cartan Theory
Teleparallelism
Yang’s Theory of Gravity
BRST Quantization of Gravity
Gravitational Instantons
Three-Dimensional Gravity
Spinor Bundles
Chiral Anomalies
Topological SL(5,R) Gauge-Invariant Action
Geometrodynamics and Its Extensions
Color Geometrodynamics
Geometric Model of Quark Confinement?