Related papers: Coherent representation of fields and deformation …
Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general…
We develop a theoretical framework for the exploration of quantum mechanical coherent population transfer phenomena, with the ultimate goal of constructing faithful models of devices for classical and quantum information processing…
The usual mathematical formalism of quantum field theory is non-rigorous because it contains divergences that can only be renormalized by non-rigorous mathematical methods. The purpose of this paper is to present a method of subtraction of…
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current…
The phase space representation for a q-deformed model of the quantum harmonic oscillator is constructed. We have found explicit expressions for both the Wigner and Husimi distribution functions for the stationary states of the…
We present a general formalism for giving a measure space paired with a separable Hilbert space a quantum version based on normalized positive operator-valued measure. The latter are built from families of density operators labelled by…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
Relation between Bopp-Kubo formulation and Weyl-Wigner-Moyal symbol calculus, and non-commutative geometry interpretation of the phase space representation of quantum mechanics are studied. Harmonic oscillator in phase space via creation…
The paper is devoted to integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also…
A $q$-deformed Weyl-Heisenberg algebra is used to define a deformed displacement operator giving rise to a naturally normalized nonlinear coherent states type. Robust maximally entangled deformed coherent states are studied and the effect…
Why do we need quantization to describe vision? What are the quadrature operators of the electromagnetic field? Is it possible to measure them? What are the characteristic functions useful for? In this brief tutorial we provide the…
In this article we study the quantization of a free real scalar field on a class of noncommutative manifolds, obtained via formal deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals…
We extend the wide-sense spatial stationarity concept of coherence holography in the regime of phase-space using the wigner distribution function. We focus mainly on the incoherent light source and the Fourier and Fresnel propagation…
We analyze the polymer representation of quantum mechanics within the deformation quantization formalism. In particular, we construct the Wigner function and the star-product for the polymer representation as a distributional limit of the…
Using the Wigner distribution function, we analyze the behavior on phase space of generalized coherent states associated with the Morse potential (Morse-like coherent states). Within the f-deformed oscillator formalism, such states are…
I review the realistic interpretation of several typically quantum phenomena using a heuristic approach that rests on the assumption that the electromagnetic quantum vacuum is a stochastic field. I include the particle behaviour of light,…
Quantum--mechanical operators corresponding to canonical momentum and position of a point--like particle, which follow from the quantum field theory in the general Riemannian space-time, satisfy generally to a deformation of the canonical…
We present a general unified approach for finding the coherent states of polynomially deformed algebras such as the quadratic and Higgs algebras, which are relevant for various multiphoton processes in quantum optics. We give a general…
Quantum field theory in the $4$-dimensional de Sitter space-time is constructed in the ambient space formalism in a rigorous mathematical framework. This work is based on the group representation theory and the analyticity of the…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…