Akifumi Sako

Deformation Quantization of Gauge theories with Separation of Variables

A noncommutative gauge theory in a homogeneous K\"ahler space is constructed.
Its noncommutative deformation is done by using deformation quantization with separation of variables which is formulated by Karabegov. This is achieved to make vector fields as inner derivations. We construct the gauge theory in homogeneous manifolds whose covariant derivatives are given by vector fields. As examples, we construct the noncommutative gauge theory in ${\mathbb C}P^N$ and ${\mathbb C}H^N$ with explicit expression.