Related papers: Deformation Quantization and Reduction by Stages

In the first part of this article we provide a geometrically oriented approach to the theory of orbispaces which originally had been introduced by Chen. We explain the notion of a vector orbibundle and characterize the good sections of a…

The purpose of this paper is to apply deformation quantization to the study of the coadjoint orbit method in the case of real reductive groups. We first prove some general results on the existence of equivariant deformation quantization of…

This paper investigates the representation-theoretic structure of the Koszul cohomology of a smooth projective variety $X$ over an algebraically closed field $k$, admitting an action of a finite group $G$ of order coprime to ${\rm…

In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases…

In this note, we study Schwarz's conjecture on application of Q-algebras to strict quantization. We prove that in the case of a torus with a constant Poisson structure, Schwarz's formalism gives the same star product as Rieffel…

Given one quasi-smooth derived space cut out of another by a section of a 2-term complex of bundles, we give two formulae for its virtual cycle. They are modelled on the the $p$-fields construction of Chang-Li and the Quantum Lefschetz…

It is proved that the (volume and orientation-preserving) quantum isometry group of a spectral triple obtained by deformation by some dual unitary 2-cocycle is isomorphic with a similar twist-deformation of the quantum isometry group of the…

Quantum phase is not a direct observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability…

Motivated by certain concepts introduced by the Refined Algebraic Quantization formalism for constrained systems which has been successfully applied within the context of Loop Quantum Gravity, in this paper we propose a phase space…

A simple mapping procedure is presented by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed directly into those in curved space with torsion. Our procedure evolved from…

It is shown how Seiberg-Witten equations can be obtained by means of Fedosov deformation quantization of endomorphism bundle and the corresponding theory of equivalences of star products. In such setting, Seiberg-Witten map can be…

Let $M$ be an arbitrary complex manifold and let $L$ be a Hermitian holomorphic line bundle over $M$. We introduce the Berezin-Toeplitz quantization of the open set of $M$ where the curvature on $L$ is non-degenerate. The quantum spaces are…

I have chosen, in this presentation of Deformation Quantization, to focus on 3 points: the uniqueness --up to equivalence-- of a universal star product (universal in the sense of Kontsevich) on the dual of a Lie algebra, the cohomology…

Structure of cold dense stellar matter at subnuclear densities is investigated with quantum molecular dynamics (QMD). We succeeded in showing that the phases with slab-like and rod-like nuclei etc. can be formed dynamically without any…

In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…

Experimentally observable Quantum Accelerator Modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes are shown to correspond to metastable…

We use Berezin's quantization procedure to obtain a formal $U_q su_{1,1}$-invariant deformation of the quantum disc. Explicit formulae for the associated q-bidifferential operators are produced.

We demonstrate that a tensor product structure could be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using classical fields modulated with pseudorandom phase sequences, we discuss…

Geometric Quantization is a term used to describe a wide collection of techniques dating back to the 1960s in the work of Kirillov, Kostant, and Souriau, which take symplectic manifolds and produce complex vector spaces. The name comes from…

This paper studies the quantization of the deformation of Hessian structures on a two-dimensional vector space, in the framework of Koszul-Vinberg algebras. We analyze how Hessian structures can be deformed to obtain quantum structures…