Deformaion Quantization with Separation of Variables for Complex Two-Dimensional Locally Symmetric Kähler Manifold
- 1 January 2022
- journal article
- research article
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Journal of Geometry and Symmetry in Physics
- Vol. 64, 39-50
- https://doi.org/10.7546/jgsp-64-2022-39-49
Abstract
A construction methods of noncommutative locally symmetric Kahler manifolds via a deformation quantization with separation of variables was proposed by SakoSuzuki-Umetsu and Hara-Sako. This construction gives the recurrence relations to determine the star product. These recurrence relations were solved for the case of the arbitrary one-dimensional ones, N-dimensional complex space, complex projective space and complex hyperbolic space. For any two-dimensional case, authors found the solution of the recurrence relations. In this paper, we review the solution and make the star product for two-dimensional complex projective space as a concrete example of this solution.Keywords
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