Related papers: Fedosov Star-Products and 1-Differentiable Deforma…

We show that for every vector bundle E over any given symplectic manifold M there exists an explicitly given super-Poisson bracket on the space of sections of the dual Grassmann bundle associated to E built out of symplectic structure of M,…

We expose the basics of the Fedosov quantization procedure, placed in the general framework of symplectic ringed spaces. This framework also includes some Poisson manifolds with non regular Poisson structures, presymplectic manifolds,…

Adopting a purely group-theoretical point of view, we consider the star product of functions which is associated, in a natural way, with a square integrable (in general, projective) representation of a locally compact group. Next, we show…

(Bi)modules, morphisms and reduction of star-products are studied in a framework of multidifferential operators along maps: morphisms deform Poisson maps and representations on functions spaces deform coisotropic maps. If a star-product is…

In this paper is considered a problem of defining natural star-products on symplectic manifolds, admissible for quantization of classical Hamiltonian systems. First, a construction of a star-product on a cotangent bundle to an Euclidean…

The notion of a local line bundle on a manifold, classified by 2-cohomology with real coefficients, is introduced. The twisting of pseudodifferential operators by such a line bundle leads to an algebroid with elliptic elements with…

We determine infinitesimal star products on Poisson manifolds compatible with coisotropic reduction. This is achieved by computing the second constraint Hochschild cohomology of the constraint algebra of functions associated to any…

It is shown that the normalized trace of Fedosov star product for quantum moment map depends only on the path component in the cohomology class of the symplectic form and the cohomology class of the closed formal 2-form required to define…

A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pure algebraic reformulation giving the…

In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form…

We give an invariant formula for a star product with separation of variables on a pseudo-Kahler manifold.

To each natural deformation quantization on a Poisson manifold M we associate a Poisson morphism from the formal neighborhood of the zero section of the cotangent bundle to M to the formal neighborhood of the diagonal of the product M x M~,…

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…

We study the general form of the noncommutative associative product (the star-product) on the Grassman algebra; the star-product is treated as a deformation of the usual "pointwise" product. We show that up to a similarity transformation,…

In this paper the deformation quantization is constructed in the case of scalar fields on Minkowski space-time. We construct the star products at three level concerning fields, Hamiltonian functionals and their underlying structure called…

Given a holomorphic Hermitian vector bundle and a star-product with separation of variables on a pseudo-Kaehler manifold, we construct a star product on the sections of the endomorphism bundle of the dual bundle which also has the…

For compact quantizable K\"ahler manifolds certain naturally defined star products and their constructions are reviewed. The presentation centers around the Berezin-Toeplitz quantization scheme which is explained. As star products the…

A star-product formalism describing deformations of the standard quantum mechanical harmonic oscillator is introduced. A number of existing generalized oscillators occur as particular choises of star-products between the elements of the…

We consider the Poisson sigma model associated to a Poisson manifold. The perturbative quantization of this model yields the Kontsevich star product formula. We study here the classical model in the Hamiltonian formalism. The phase space is…

We show that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero, determines the individual constituents uniquely. This is analogous to the uniqueness of prime…