Related papers: To what extent are canonical and coherent state qu…
We perform canonical quantization of General Relativity, as an effective quantum field theory below the Planck scale, within the BRST-invariant framework. We show that the promotion of constraints to dynamical equations of motion for…
In~this paper, we construct noncommutative coherent states using various families of unitary irreducible representations (UIRs) of $\g$, a connected, simply connected nilpotent Lie group, that was identified as the kinematical symmetry…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…
We employ the familiar canonical quantization procedure in a given cosmological setting to argue that it is equivalent to and results in the same physical picture if one considers the deformation of the phase-space instead. To show this we…
Classical Koopman--von Neumann Hilbert spaces of states are constructed here by the action of classical random fields on a vacuum state in ways that support an action of the quantized electromagnetic field and of the $U(1)$--invariant…
We present a list of formulae useful for Weyl-Heisenberg integral quantizations, with arbitrary weight, of functions or distributions on the plane. Most of these formulae are known, others are original. The list encompasses particular cases…
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the two approaches are in good agreement, we…
The quantum state is a mathematical object used to determine the outcome probabilities of measurements on physical systems. Its fundamental nature has been the subject of discussions since the origin of the theory: is it ontic, that is,…
In this survey, various generalisations of Glauber-Sudarshan coherent states are described in a unified way, with their statistical properties and their possible role in non-standard quantisations of the classical electromagnetic field.…
The original canonical coherent states could be defined in several ways. As applications for other sets of coherent states arose, the rules of definition were correspondingly changed. Among such rule changes were a change of group and…
Non-Gaussian quantum states of light are essential resources for quantum information processing and precision metrology. Among them, generalized coherent states (GCS), which naturally arise from the evolution of a coherent state with a…
The approach of Berezin to the quantization of so(n,2) via generalized coherent states is considered in detail. A family of n commuting observables is found in which the basis for an associated Fock-type representation space is expressed.…
We present a detailed report on the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments. The rate…
In this paper we construct manifestly covariant relativistic coherent states on the entire complex plane which reproduce others previously introduced on a given $SL(2,R)$ representation, once a change of variables $z\in C\rightarrow z_D \in…
We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…
It is commonly claimed in the recent literature that certain solutions to wave equations of positive energy of Dirac-type with internal variables are characterized by a non-thermal spectrum. As part of that statement, it was said that the…
Unique set of coherent states for the anharmonic oscillator is obtained by requiring i. under the quantum mechanical time evolution a coherent state evolves into another, governed by trajectory in the classical phase space (of a related…
Since the uncertainty about an observable of a system prepared in a quantum state is usually described by its variance, when the state is mixed, the variance is a hybrid of quantum and classical uncertainties. Besides that, complementarity…
Based on the definition of coherent states for continuous spectra and analogous to photon added coherent states for discrete spectra, we introduce the excited coherent states for continuous spectra. It is shown that, the main axioms of…
This work mainly addresses a construction of Gazeau-Klauder type coherent states for a P\"oschl-Teller model. Relevant characteristics are investigated. Induced geometry and statistics are studied. Then the Berezin - Klauder - Toeplitz…