Related papers: Deformation quantization of contact manifolds
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
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 preprint the notion of deformation quantization of endomorphism bundles over symplectic manifolds is defined and developed, including index theory.
We introduce the classes of holomorphic $p$-contact manifolds and holomorphic $s$-symplectic manifolds that generalise the classical holomorphic contact and holomorphic symplectic structures. After observing their basic properties and…
We construct (infinitely many) examples in all dimensions of contactomorphisms of closed overtwisted contact manifolds that are smoothly isotopic but not contact-isotopic to the identity.
Basic properties of even (odd) supermanifolds endowed with a connection respecting a given symplectic structure are studied. Such supermanifolds can be considered as generalization of Fedosov manifolds to the supersymmetric case.
Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…
This is a survey on our recent works which reveal new relationships among deformation quantization, geometric quantization, Berezin-Toeplitz quantization and BV quantization on K\"ahler manifolds.
The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a canonical sheaf of categories deforming coherent…
Fedosov has described a geometro-algebraic method to construct in a canonical way a deformation of the Poisson algebra associated with a finite-dimensional symplectic manifold ("phase space"). His algorithm gives a non-commutative, but…
We give an explicit construction of a deformation quantization of the algebra of functions on a Poisson manifolds, based on Kontsevich's local formula. The deformed algebra of functions is realized as the algebra of horizontal sections of a…
We discuss the deformation quantization approach for the teaching of quantum mechanics. This approach has certain conceptual advantages which make its consideration worthwhile. In particular, it sheds new light on the relation between…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
A method for the deformation quantization of coadjoint orbits of semisimple Lie groups is proposed. It is based on the algebraic structure of the orbit. Its relation to geometric quantization and differentiable deformations is explored.
The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold $\mathcal M$ is presented as a…
This note describes the functional-integral quantization of two-dimensional topological field theories together with applications to problems in deformation quantization of Poisson manifolds and reduction of certain submanifolds. A brief…
The goal of this note is to describe a class of formal deformations of a symplectic manifold $M$ in the case when the base ring of the deformation problem involves parameters of non-positive degrees. The interesting feature of such…
The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to…
The Fedosov deformation quantization on a cotangent bundle with a symplectic connection induced by some linear symmetric connection on the base space is considered. A global construction of the symplectic homogeneous connection on the…
We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the connected components of the strict contactomorphism group which…