Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms

Details Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms

2010-01-04

arxiv.org/abs/1001.0508v3

Phys. Rev. D81:085026,2010

Physics

High Energy Physics

High Energy Physics - Theory

AMS-LaTeX 19 pages. v2: corrections in language and equations (typos), expanded sections 3-5, added references. v3: minor pres

Scientific paper

10.1103/PhysRevD.81.085026

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.

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