Deformation Quantization with Separation of Variables and Gauge Theories

Abstract

We construct a gauge theory on a noncommutative homogeneous Kahler manifold by using the deformation quantization with separation of variables for Kahler 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 \( \mathbb{C}P^N \) and construct a gauge theory on it. We also give details of the proof showing that the noncommutative \( \mathbb{C}P^N \) constructed in this paper coincides with the one given by Bordemann, Brischle, Emmrich and Waldmann [1].