Geometrodynamics Of Gauge Fields: On The Geometry Of Yang-mills And Gravitational Gauge Theories (mathematical Physics Studies)
by Eckehard W. Mielke /
2017 / English / PDF
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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.
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.
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.