publication . Other literature type . Article . Preprint . 2016

On the phase form of a deformation quantization with separation of variables

Karabegov, Alexander;
  • Published: 01 Jun 2016
  • Publisher: Elsevier BV
Given a star product with separation of variables on a pseudo-Kaehler manifold, we obtain a new formal (1,1)-form from its classifying form and call it the phase form of the star product. The cohomology class of a star product with separation of variables equals the class of its phase form. We show that the phase forms can be arbitrary and they bijectively parametrize the star products with separation of variables. We also describe the action of a change of the formal parameter on a star product with separation of variables, its formal Berezin transform, classifying form, phase form, and canonical trace density.
arXiv: Astrophysics::Galaxy AstrophysicsAstrophysics::Solar and Stellar Astrophysics
free text keywords: Mathematical Physics, General Physics and Astronomy, Geometry and Topology, Separation of variables, Topology, A* search algorithm, law.invention, law, Star product, Manifold, Berezin transform, Mathematics, Deformation (mechanics), Cohomology, Quantization (signal processing), Mathematical analysis, Mathematics - Quantum Algebra, 53D55
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