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29 March 2024
 
  » arxiv » gr-qc/9407031

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Yang--Mills Configurations from 3D Riemann--Cartan Geometry
E.W. Mielke ; Y.N. Obukhov ; F.W. Hehl ;
Date 21 Jul 1994
Journal Phys.Lett. A192 (1994) 153-162
Subject gr-qc hep-th
AbstractRecently, 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.
Source arXiv, gr-qc/9407031
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