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

Original · EN

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).