Related papers: Tomographic Representation of Minisuperspace Quant…
Quantum and classical physical states are represented in a unified way when they are described by symplectic tomography. Therefore this representation allows us to study directly the necessary conditions for a classical universe to emerge…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum Foundations and Quantum Information such…
The importance of the tomographic approach is that either in quantum mechanics as in classical mechanics the state of a physical system is expressed with the same family of functions, the tomograms. The extension of this procedure to…
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
Recently, a new framework for describing the multiverse has been proposed which is based on the principles of quantum mechanics. The framework allows for well-defined predictions, both regarding global properties of the universe and…
We study the evolution of a two dimensional minisuperspace cosmological model in classical and quantum levels by the Noether symmetry approach. The phase space variables turn out to correspond to the scale factor of a…
Within the framework of the probability representation of quantum mechanics, we study a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides; in other words, the cyclic groups (containing the…
This article examines the analytic solutions of isotropic spacetime with the minimal coupling of scalar field and matter in the context of energy-momentum squared gravity. The scalar field includes quintessence and phantom dark energy…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or…
In this paper, based on the works of Capozziello et al., we have studied the Noether symmetry approach in the cosmological model with scalar and gauge fields proposed recently by Soda et al. The correct Noether symmetries and related Lie…
We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and…
It is now well established that quantum tomography provides an alternative picture of quantum mechanics. It is common to introduce tomographic concepts starting with the Schrodinger-Dirac picture of quantum mechanics on Hilbert spaces. In…
On the base of symplectic quantum tomogram we define a probability distribution on the plane. The dual map transfers all observables which are polynomials of the position and momentum operators to the set of polynomials of two variables. In…
In the framework of scalar-tensor gravity, we consider non-flat interacting quintessence cosmology where a scalar field is interacting with dark matter. Such a scalar field can be a standard or a phantom one. We use the Noether Symmetry…
We study the metric $f(R)$ cosmology using Noether symmetry approach by utilizing the behavior of the corresponding Lagrangian under infinitesimal generators of the desired symmetry. The existence of Noether symmetry of the cosmological…
We propose a model for noncommutative quantum cosmology by means of a deformation of minisuperspace. For the Kantowski-Sachs metric we are able to find the exact wave function. We construct wave packets and show that new quantum states that…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…