Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms
High Energy Physics - Theory
2014-11-20 v3 General Relativity and Quantum Cosmology
Abstract
We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restrictions imposed by the associativity property of the star product, the torsion of the space-time has to be covariant constant. An illustrative example is given and it is concluded that in this case the conditions necessary to define a covariant star product on a symplectic manifold completely determine its connection.
Cite
@article{arxiv.1001.0508,
title = {Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms},
author = {M. Chaichian and M. Oksanen and A. Tureanu and G. Zet},
journal= {arXiv preprint arXiv:1001.0508},
year = {2014}
}
Comments
AMS-LaTeX 19 pages. v2: corrections in language and equations (typos), expanded sections 3-5, added references. v3: minor presentational and grammatical corrections, completed, corrected and reordered some references.