Explicit Formulae for Noncommutative Deformations of CP^N and CH^N

Akifumi Sako, Toshiya Suzuki, Hiroshi Umetsu

Published 2012-04-18, updated 2012-06-01Version 2

We give explicit expressions of a deformation quantization with separation of variables for CP^N and CH^N. This quantization method is one of the ways to perform a deformation quantization of Kahler manifolds, which is introduced by Karabegov. Star products are obtained as explicit formulae in all order in the noncommutative parameter. We also give the Fock representations of the noncommutative CP^N and CH^N.