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We give an explicit local formula for any formal deformation quantization, with separation of variables, on a Kahler manifold. The formula is given in terms of differential operators, parametrized by acyclic combinatorial graphs.
Deformation quantization conventionally is described in terms of multidifferential operators. Jet manifold technique is well-known provide the adequate formulation of theory of differential operators. We extended this formulation to the multidifferen
We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus: noncommutative symbolic calculus, the principal symbol, and the
We consider formal deformations of the Poisson algebra of functions (with singularities) on $T^*M$ which are Laurent polynomials of fibers. Tn the case: $dim M=1$ ($M=S^1, {bf R}$), there exists a non-trivial $star$-product on this algebra non-equivalent to the standard Moyal product.
We use a deformed differential structure to obtain a curved metric by a deformation quantization of the flat space-time. In particular, by setting the deformation parameters to be equal to physical constants we obtain the Friedmann-Robertson-Walker (
In this semi-expository paper we study two examples of coherent states based on the Weyl- Heisenberg group and the group of $2 times 2$ upper triangular matrices. It is known that sometimes the coherent states provide us with a Kahler embedding of a