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.Comment: 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