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Geometrodynamics of Gauge Fields
On the Geometry of Yang-Mills and Gravitational Gauge Theories
Englisch
333 b
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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.§
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