Related papers: Quantization of the sphere with coherent states
In this paper, we study the role of coherent states in the realm of quantum cosmology, both in a second-quantized single universe and in a third-quantized quantum multiverse. In particular, most emphasis will be paid to the quantum…
A fully geometric procedure of quantization that utilizes a natural and necessary metric on phase space is reviewed and briefly related to the goals of the program of geometric quantization.
The characterization of the quantum ensemble is a fundamental issue in quantum information theory and foundations. The ensemble is also useful for various quantum information processing. To characterize the quantum ensemble, in this…
We outline the principal results of a recent examination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration. Two examples serve to illustrate the…
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
We introduce a measure of ''quantumness'' for any quantum state in a finite dimensional Hilbert space, based on the distance between the state and the convex set of classical states. The latter are defined as states that can be written as a…
The domain of application of quantization methods is traditionally restricted to smooth classical observables. We show that the coherent states or "anti-Wick" quantization enables us to construct fairly reasonable quantum versions of…
We formulate a relation between quantum-mechanical coherent states and complex-differentiable structures on the classical phase space ${\cal C}$ of a finite number of degrees of freedom. Locally-defined coherent states parametrised by the…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to…
We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated…
Quantum Space-Time and Phase Space with fuzzy geometric structure are studied as possible formalism for quantization of massive particles and fields. In this approach the state of nonrelativistic particle m described by the fuzzy point of…
Generalized coherent states for shape invariant potentials are constructed using an algebraic approach based on supersymmetric quantum mechanics. We show this generalized formalism is able to: a) supply the essential requirements necessary…
The fuzzy sphere, as a quantum metric space, carries a sequence of metrics which we describe in detail. We show that the Bloch coherent states, with these spectral distances, form a sequence of metric spaces that converge to the round…
Phase operators are constructed using a Klauder-Berezin coherent state quantization in finite Hilbert subspaces of the Hilbert space of Fourier series. The study of infinite dimensional limits of mean values of some observables phase leads…
The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a (coherent-state) phase-space path integral, and at…
Quantum versions of cylindric phase space, like for the motion of a particle on the circle, are obtained through different families of coherent states. The latter are built from various probability distributions of the action variable. The…
The present article is primarily a review of the projection-operator approach to quantize systems with constraints. We study the quantization of systems with general first- and second-class constraints from the point of view of…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…