Related papers: Canonical transforms, quantumness and probability …
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the…
The time dependence of one-dimensional quantum mechanical probability densities is presented when the potential in which a particle moves is suddenly changed, called a quench. Quantum quenches are mainly addressed but a comparison with…
The paper discusses the physical groundlessness of the models used for the derivation of canonical distribution and provides the experimental data demonstrating the incompleteness of quantum mechanics. The possibility of using statistical…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
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…
The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free…
Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A…
At large quantum numbers, the probability densities for particle-in-a-box or simple harmonic oscillator converge to the classical result upon coarse-graining the quantum mechanical probability densities by introducing a finite resolution in…
We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
A homogeneous and isotropic cosmological model with a positive cosmological constant is considered. The matter sector is given by a massless scalar field, which can be used as an internal time to deparametrize the theory. The idea is to…
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…
In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…
Review of tomographic probability representation of quantum states is presented both for oscillator systems with continious variables and spin--systems with discrete variables. New entropic--information inequalities are obtained for…
Probability representation entropy (tomographic entropy) of arbitrary quantum state is introduced. Using the properties of spin tomogram to be standard probability distribution function the tomographic entropy notion is discussed. Relation…
Quantum mechanics is reformulated using Hartle's definition of the state of an individual physical system and a variant of von Neumann's propositional calculus. An elementary set of quantum postulates lead inductively to the familiar…
Some of the important non-classical aspects of quantum mechanics can be described in more intuitive terms if they are reformulated in a geometrical picture based on an extension of the classical phase space. This contribution presents…
Recently, a geometric embedding of the classical space and classical phase space of an n-particle system into the space of states of the system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the…
Several finite dimensional quasi-probability representations of quantum states have been proposed to study various problems in quantum information theory and quantum foundations. These representations are often defined only on restricted…