Yang--Mills Configurations from 3D Riemann--Cartan Geometry

Abstract

Recently, the {\it spacelike} part of the $SU(2)$ Yang--Mills equations has been identified with geometrical objects of a three--dimensional space of constant Riemann--Cartan curvature. We give a concise derivation of this Ashtekar type (``inverse Kaluza--Klein") {\it mapping} by employing a $(3+1)$--decomposition of {\it Clifford algebra}--valued torsion and curvature two--forms. In the subcase of a mapping to purely axial 3D torsion, the corresponding Lagrangian consists of the translational and Lorentz {\it Chern--Simons term} plus cosmological term and is therefore of purely topological origin.

14 pages, preprint Cologne-thp-1994-h10

References in corpus (3)

• The Hidden Spatial Geometry of Non-Abelian Gauge Theories
• Ashtekar's New Variables and Positive Energy
• QCD Originated Dynamical Symmetry for Hadrons

Cited by in corpus (12)

• Metric-Affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance
• A gauge-invariant Hamiltonian analysis for non-Abelian gauge theories in (2+1) dimensions
• Planar Yang-Mills theory: Hamiltonian, regulators and mass gap
• Symmetric Space Cartan Connections and Gravity in Three and Four Dimensions
• On the Gauge Aspects of Gravity
• Yang-Mills Theory in 2+1 Dimensions: Coupling of Matter Fields and String-breaking Effects
• The robustness of the vacuum wave function and other matters for Yang-Mills theory
• Reformulation of QCD in the language of general relativity
• Vacuum Einstein Equations in Terms of Curvature Forms
• Spatial Geometry of Non-Abelian Gauge Theory in \(2 + 1\) Dimensions
• Space-Time Geometry of Three-Dimensional Yang-Mills Theory
• Extended Schouten classification for non-Riemannian geometries