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

E. W. Mielke·Y. N. Obukhov·F. W. Hehl
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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.

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E. W. Mielke, Y. N. Obukhov, F. W. Hehl. 1994-07-21. Yang--Mills Configurations from 3D Riemann--Cartan Geometry. https://doi.org/10.1016/0375-9601(94)90237-2

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