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

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

2002-06-25

arxiv.org/abs/math/0206271v2

Mathematics

Quantum Algebra

9 pages, minor typos corrected

Scientific paper

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).

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