Related papers: Quantization via Deformation of Prequantization

A geometric prequantization formula for the Poisson-Gerstenhaber bracket of forms found within the DeDonder-Weyl Hamiltonian formalism earlier is presented. The related aspects of covariant geometric quantization of field theories are…

A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…

In this article we consider quantum phase space reduction when zero is a regular value of the momentum map. By analogy with the classical case we define the BRST cohomology in the framework of deformation quantization. We compute the…

Let X be a compact connected Riemann surface of genus g > 0 equipped with a nonzero holomorphic 1-form. Let M denote the moduli space of semistable Higgs bundles on X of rank r and degree r(g-1)+1; it is a complex symplectic manifold. Using…

We study the deformation quantisation (Moyal quantisation) of general constrained Hamiltonian systems. It is shown how second class constraints can be turned into first class quantum constraints. This is illustrated by the O(N) non-linear…

This dissertation is an exposition of Kontsevich's proof of the formality theorem and the classification of deformation quantisation on a Poisson manifold. We begin with an account of the physical background and introduce the Weyl-Moyal…

A model of 3-dimensional topological quantum field theory is rigorously constructed. The results are applied to an explicit formula for deformation quantization of any finite-dimensional Lie bialgebra over the field of complex numbers. This…

We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components…

Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…

Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…

The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…

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…

Spectral transformation is known to set up a birational morphism between the Hitchin and Beauville-Mukai integrable systems. The corresponding phase spaces are: (a) the cotangent bundle of the moduli space of bundles over a curve C, and (b)…

Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…

Our aim in this thesis is to use the language of deformation-quantization to understand certain quantized algebras by looking at properties of the corresponding commutative ones, and conversely to obtain results about the commutative…

Generalizing deformation quantizations with separation of variables of a K\"ahler manifold $M$, we adopt Fedosov's gluing argument to construct a category $\mathsf{DQ}$, enriched over sheaves of $\mathbb{C}[[\hbar]]$-modules on $M$, as a…

Starting from deformation quantization (star-products), the quantization problem of Nambu Mechanics is investigated. After considering some impossibilities and pushing some analogies with field quantization, a solution to the quantization…

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…

We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation q uantizations equivariant under the action of $G$ and the corresponding quantum group. We…

In this work, we present straightforward and concrete computations of the unitary irreducible representations of the Euclidean motion group $M(2)$ employing the methods of deformation quantization. Deformation quantization is a quantization…