Related papers: Effective Space Quantization in Friedman-Robertson…

We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of…

The equivalence postulate approach to quantum mechanics aims to formulate quantum mechanics from a fundamental geometrical principle. Underlying the formulation there exists a basic cocycle condition which is invariant under…

In this work, we present an overview of uniqueness results derived in recent years for the quantization of Gowdy cosmological models and for (test) Klein-Gordon fields minimally coupled to Friedmann-Lema\^{\i}tre-Robertson-Walker, de…

Two approaches to quantization of Freedman's closed Universe are compared. In the first approach, the Shrodinger's norm of the wave function of Universe is used, and in the second approach, the Klein-Gordon's norm is used. The second one…

Ambiguities arising in different approaches (canonical, quasiclassical, path integration) to quantization are discussed by an example of the mechanics of a point-like particle in the Riemannian space (the geodesic dynamics). A way to select…

Classical mechanics, in the Koopman-von Neumann formulation, is described in Hilbert space. It is shown here that classical canonical transformations are generated by Hermitian operators that are in general noncommutative. This naturally…

Doplicher, Fredenhagen, and Roberts (1994, 1995) proposed a simple model of a particle in quantum spacetime. We give a new formulation of the model and propose some small changes and additions which improve the physical interpretation. In…

Quantum cosmological models are commonly described by means of semiclassical approximations in which a smooth evolution of the expectation values of elementary geometry operators replaces the classical and singular dynamics. The advantage…

We consider the conditioning of the timeless solution to the Wheeler-DeWitt equation by a predefined matter clock state in the simple scenario of de Sitter universe. The resulting evolution of the geometrodynamical degree of freedom with…

In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The…

Perturbative quantum gravity in the framework of the Schwinger-Keldysh formalism is applied to compute lowest-order corrections to the actual expansion of the Universe described in terms of the spatially flat…

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.…

The Newton equation describing the particle motion in constant external field force on canonical, Lie-algebraic and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent,…

The aim of this paper is to give a basic overview of Deformation Quantization (DQ) to physicists. A summary is given here of some of the key developments over the past thirty years in the context of physics, from quantum mechanics to…

We propose that the size of the universe and its rate of expansion cannot be simultaneously specified with arbitrary precision, a quantum mechanical statement encoded in a deformed commutation relation for the scale factor. The deformation…

Deformation quantization is applied to quantize gravitational systems coupled with matter. This quantization procedure is performed explicitly for quantum cosmology of these systems in a flat minisuper(phase)space. The procedure is employed…

We describe a deformation of the observable algebra of quantum gravity in which the loop algebra is extended to framed loops. This allows an alternative nonperturbative quantization which is suitable for describing a phase of quantum…

In this work, first, we study a flat Friedmann-Robertson-Walker Universe with two scalar fields but only one potential term, which can be thought as a simple quintessence plus a K-essence model. Employing the Hamiltonian formalism we are…

We study the classical and quantum models of a flat Friedmann-Robertson-Walker (FRW) space-time, coupled to a perfect fluid, in the context of the consensus and a gauge-fixed Lagrangian frameworks. It is shown that, either in the usual or…

In this paper we study quantum dynamics of the bouncing cosmological model. We focus on the model of the flat Friedman-Robertson-Walker universe with a free scalar field. The bouncing behavior, which replaces classical singularity, appears…