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Mathematical Physics Studies

Geometrodynamics of Gauge Fields

On the Geometry of Yang-Mills and Gravitational Gauge Theories

Authors: Mielke, Eckehard W.

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  • 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
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eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-29734-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA in USD
  • ISBN 978-3-319-29732-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA in USD
  • ISBN 978-3-319-80638-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

Eckehard Mielke has been Professor in the Department of Physics, Universidad Autónoma Metropolitana-Iztapalapa, Mexico since 1997.  His work has covered the Wheeler-DeWitt equation, knot theory and wormholes, conformal changes of metrics, Poincaré gauge theory and its metric-affine generalizations, double dual solutions, topological models of gravity with Chern-Simons terms, Ashtekar variables, boson stars, dark matter, and inflationary cosmology.

He is the author of the Springer book "Sonne, Mond und .... Schwarze Locher" (1997) (Sun, Moon and...Black Holes), a popular book offering a short trip through recent developments in astronomy.

Table of contents (16 chapters)

Table of contents (16 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-3-319-29734-7
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA in USD
  • ISBN 978-3-319-29732-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA in USD
  • ISBN 978-3-319-80638-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometrodynamics of Gauge Fields
Book Subtitle
On the Geometry of Yang-Mills and Gravitational Gauge Theories
Authors
Series Title
Mathematical Physics Studies
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29734-7
DOI
10.1007/978-3-319-29734-7
Hardcover ISBN
978-3-319-29732-3
Softcover ISBN
978-3-319-80638-9
Series ISSN
0921-3767
Edition Number
2
Number of Pages
XVII, 373
Number of Illustrations
10 b/w illustrations, 8 illustrations in colour
Topics