Related papers: An introduction to strict quantization
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…
In this paper we study a gradient flow approach to the problem of quantization of measures in one dimension. By embedding our problem in $L^2$, we find a continuous version of it that corresponds to the limit as the number of particles…
An approach to quantization of fields and gravity based on the De Donder-Weyl covariant Hamiltonian formalism is outlined. It leads to a hypercomplex extension of quantum mechanics in which the algebra of complex numbers is replaced by the…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
In this review we attempt to present an overview of some of the better known quantization techniques found in the current literature and used both by physicists and mathematicians. The treatment is more descriptive than rigorous, for we aim…
This note aims to subsume several apparently unrelated models under a common framework. Several examples of well-known quantum field theories are listed which are connected via stochastic quantization. We highlight the fact that the…
A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools…
We explain the powerful role that operator-valued measures can play in quantizing any set equipped with a measure, for instance a group (resp. group coset) with its invariant (resp. quasi-invariant) measure. Coherent state quantization is a…
Using general construction of star-product the q-deformed Wigner-Weyl-Moyal quantization procedure is elaborated. The q-deformed Groenewold kernel determining the product of quantum observables is given in explicit form for small…
We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics. We then discuss prequantization, and go into…
The use of the quantizer-dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an…
We use a natural affine connection with nontrivial torsion on an arbitrary almost-Kaehler manifold which respects the almost-Kaehler structure to construct a Fedosov-type deformation quantization on this manifold.
Deformation quantization of bosonic strings is considered. We show that the light-cone gauge is the most convenient classical description to perform the quantization of bosonic strings in the deformation quantization formalism. Similar to…
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 four-parameter deformation of continued fractions, which we call $ U $-deformation. We study some particular cases and compare them with the q-deformation of continued fractions introduce recently by Morier-Genoud and…
The main objective of this article is to develop the theory of deformation of $C^*$-algebras endowed with a group action, from the perspective of non-formal equivariant quantization. This program, initiated in \cite{Bieliavsky-Gayral}, aims…
Motivated by the compactification process of the space of connections in loop quantum gravity literature. A description of the space of G-connections using the tangent groupoid is given. As the tangent groupoid parameter is away from zero,…
We first generalise the standard Wigner function to Dirac fermions in curved spacetimes. Secondly, we turn to the Moyal quantisation of systems with constraints. Gravity is used as an example.
In this review we discuss various aspects of representation theory in deformation quantization starting with a detailed introduction to the concepts of states as positive functionals and the GNS construction. But also Rieffel induction of…
We present explicit universal strict deformation quantization formulae for actions of Iwasawa subgroups AN of SU(1,n). This answers a question raised by Rieffel.