Related papers: Classical and quantum free motions in the tomograp…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
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…
States of nonlinear quantum oscillators (f-oscillators) are considered in the Weyl-Wigner-Moyal representation and the tomographic probability representation, where the states are described by standard probability distributions instead of…
A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After…
Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
Classical and quantum perturbations can be described in terms of marginal distribution functions in the framework of tomographic cosmology. In particular, the so called Radon transformation and the mode-parametric quantum oscillator…
A sample of some relevant developments that have taken place during the last twenty years in classical and quantum tomography are displayed. We will present a general conceptual framework that provides a simple unifying mathematical picture…
It is shown that trajectories of free motion of the particles in deformed ("quantum") four dimensional space-time are quadratic curves.
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
Among the many perplexing results of quantum mechanics is one that contradicts a result from introductory physics: the possibility of finding a quantum particle in a region that would be forbidden classically by energy conservation. An…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
We describe both quantum particles and classical particles in terms of a classical statistical ensemble, characterized by a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…
Motion of a non-relativistic particle on a cone with a magnetic flux running through the cone axis (a ``flux cone'') is studied. It is expressed as the motion of a particle moving on the Euclidean plane under the action of a…
Symplectic tomographies of classical and quantum states are shortly reviewed. The concept of nonlinear f-oscillators and their properties are recalled. The tomographic probability representations of oscillator coherent states and the…