English

A covariant Poisson deformation quantization with separation of variables up to the third order

Quantum Algebra 2007-05-23 v2

Abstract

We give a simple formula for the operator C_3 of the standard deformation quantization with separation of variables on a K\"ahler manifold M. Unlike C_1 and C_2, this operator can not be expressed in terms of the K\"ahler-Poisson tensor on M. We modify C_3 to obtain a covariant deformation quantization with separation of variables up to the third order which is expressed in terms of the Poisson tensor on M and thus can be defined on an arbitrary complex manifold endowed with a Poisson bivector field of type (1,1).

Keywords

Cite

@article{arxiv.math/0206271,
  title  = {A covariant Poisson deformation quantization with separation of variables up to the third order},
  author = {Alexander Karabegov},
  journal= {arXiv preprint arXiv:math/0206271},
  year   = {2007}
}

Comments

9 pages, minor typos corrected