Deformation quantization with separation of variables and gauge theories

Abstract

We construct a gauge theory on a noncommutative homogeneous Kähler manifold by using the deformation quantization with separation of variables for Kähler manifolds. A model of noncommutative gauge theory that is connected with an ordinary Yang-Mills theory in the commutative limit is given. As an examples, we review a noncommutative ℂPN and construct a gauge theory on it. We also give details of the proof showing that the noncommutative ℂPN constructed in this paper coincides with the one given by Bordemann, Brischle, Emmrich and Waldmann [1].