A covariant Poisson deformation quantization with separation of variables up to the third order
Alexander Karabegov
Abstract
We give a simple formula for the operator C3 of the standard deformation quantization with separation of variables on a Kähler manifold M. Unlike C1 and C2, this operator can not be expressed in terms of the Kähler-Poisson tensor on M. We modify C3 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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