相关论文: Global Non-perturbative Deformation Quantization o…

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…

We describe a deformation quantization of a modification of Poisson geometry by a closed 3-form. Under suitable conditions it gives rise to a stack of algebras. The basic object used for this aim is a kind of families of Poisson structures…

We introduce a noncommutative Poisson random measure on a von Neumann algebra. This is a noncommutative generalization of the classical Poisson random measure. We call this construction Poissonization. Poissonization is a functor from the…

For a possibly singular subset of a regular Poisson manifold we construct a deformation quantization of its algebra of Whitney functions. We then extend the construction of a deformation quantization to the case where the underlying set is…

Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on n-dimensional space taking values in a Grassmann algebra with m generating elements are described up to an equivalence…

We study the problem of deformation quantization for (algebraic) symplectic manifolds over a base field of positive characteristic. We prove a reasonably complete classification theorem for one class of such quantizations; in the course of…

A noncommutative algebra $A$, called an algebraic noncommutative geometry, is defined, with a parameter $\epsilon$ in the centre. When $\epsilon$ is set to zero, the commutative algebra $A^0$ of algebraic functions on an algebraic manifold…

In this paper we define an algebra structure on the vector space $L(\Sigma)$ generated by links in the manifold $\Sigma \times [0,1]$ where $\Sigma $ is an oriented surface. This algebra has a filtration and the associated graded algebra…

The notions of the Novikov deformation of a commutative associative algebra and the corresponding classical limit are introduced. We show such a classical limit belongs to a subclass of transposed Poisson algebras, and hence the Novikov…

Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding…

A perturbative formulation of algebraic field theory is presented, both for the classical and for the quantum case, and it is shown that the relation between them may be understood in terms of deformation quantization.

We construct a method to obtain the algebraic classification of Poisson algebras defined on a commutative associative algebra, and we apply it to obtain the classification of the $3$-dimensional Poisson algebras. In addition, we study the…

In this work, we find the Poisson superalgebras related to schemes of quantization. Initially, we consider the Dirac superbracket in the context of the quantization of constrained systems. Next, we show the existence of a Poisson…

Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables…

We place the renormalization procedure in quantum field theory into the familiar mathematical context of quantization of Poisson algebras. The Poisson algebra in question is the algebra of classical field theory Hamiltonians constructed in…

We describe two types of Poisson pencils generated by a linear bracket and a quadratic one arising from a classical R-matrix. A quantization scheme is discussed for each. The quantum algebras are represented as the enveloping algebras of…

The gauge invariant observables of the closed bosonic string are quantized without anomalies in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach. The quantum algebra is the kernel of a…

Let $\{{\cdot},{\cdot}\}_{\boldsymbol{\mathcal{P}}}$ be a variational Poisson bracket in a field model on an affine bundle $\pi$ over an affine base manifold $M^m$. Denote by $\times$ the commutative associative multiplication in the…

Let $\Gamma$ be a finite group acting faithfully and linearly on a vector space $V$. Let $T(V)$ ($S(V)$) be the tensor (symmetric) algebra associated to $V$ which has a natural $\Gamma$ action. We study generalized quadratic relations on…

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map)…