Geometrodynamics of Gauge Fields

On the Geometry of Yang-Mills and Gravitational Gauge Theories

  • Eckehard W. Mielke

Part of the Mathematical Physics Studies book series (MPST)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Eckehard W. Mielke
    Pages 1-12
  3. Eckehard W. Mielke
    Pages 13-35
  4. Eckehard W. Mielke
    Pages 37-63
  5. Eckehard W. Mielke
    Pages 65-94
  6. Eckehard W. Mielke
    Pages 95-107
  7. Eckehard W. Mielke
    Pages 109-136
  8. Eckehard W. Mielke
    Pages 137-159
  9. Eckehard W. Mielke
    Pages 161-179
  10. Eckehard W. Mielke
    Pages 181-195
  11. Eckehard W. Mielke
    Pages 197-225
  12. Eckehard W. Mielke
    Pages 227-259
  13. Eckehard W. Mielke
    Pages 261-273
  14. Eckehard W. Mielke
    Pages 293-328
  15. Eckehard W. Mielke
    Pages 329-345
  16. Eckehard W. Mielke
    Pages 347-358
  17. Back Matter
    Pages 359-373

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.


Foundations of Gauge Theory Gauge Theories in Particle Physics Gauge Theories of Gravitation Geometry of Gauge Fields Geometry of Yang-Mills Gravitational Gauge Theories Instanton Solutions Poincar_E Gauge Theory Topological Invariants Yang-Mills Theory

Authors and affiliations

  • Eckehard W. Mielke
    • 1
  1. 1.Departamento de Física, CBI IztapalapaUniversidad Autónoma MetropolitanMexico CityMexico

Bibliographic information