Related papers: Minimal Coupling in Koopman-von Neumann Theory
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
We study nonequilibrium evolution in a self-interacting quantum field theory invariant under space translation only by using a canonical approach based on the recently developed Liouville-von Neumann formalism. The method is first used to…
We extend the Quantum Memory Matrix (QMM) framework, originally developed to reconcile quantum mechanics and general relativity by treating space-time as a dynamic information reservoir, to incorporate the full suite of Standard Model gauge…
We construct quantum algorithms to compute the solution and/or physical observables of nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations (HJE) via linear representations or exact mappings between…
Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three…
The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…
Currently, dynamics of a massive macroparticle is given by classical analytical mechanics (CM), while that of a massive micro one is given by quantum mechanics (QM). We propose a mechanics effective for both: We transform, under coordinate…
A nonminimal coupling single scalar field theory, when transformed from Jordan frame to Einstein frame, can act like a minimal coupling one. Making use of this property, we investigate how a nonminimal coupling theory with scale-invariant…
This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum…
We suggest to use "minimal" choice of quantum gravity theory, that is the quantum field theory, in which space-time is seen as Riemannian space and metric (or vierbein field) is the dynamical variable. We then suggest to use the simplest…
The minimal-length paradigm, a possible implication of quantum gravity at low energies, is commonly understood as a phenomenological modification of Heisenberg's uncertainty relation. We show that this modification is equivalent to a…
In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{quantum} geometries. We initiate the development of a quantum theory of test scalar fields on these…
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation…
Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here we present different approaches to Koopman's Hilbert-space formulation of classical mechanics in the context of Vlasov-Maxwell kinetic…
Going back to the early days in the history of quantum mechanics, the interaction of quantum and classical systems stands among the most intriguing open questions in science and makes its appearance in several fields, from physics to…
Using the Gell-Mann and Hartle formalism of generalized quantum mechanics of closed systems, we study the classical limit of coarse-grained spacetime histories and their decoherence. The system under consideration is one-dimensional and…
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…
We will establish the connection between the Lorentz covariant and so-called single-time formulation for the quark Wigner operator. To this end we will discuss the initial value problem for the Wigner operator of a field theory and give a…
As is widely-known, the eigen-functions of the Landau problem in the symmetric gauge are specified by two quantum numbers. The first is the familiar Landau quantum number $n$, whereas the second is the magnetic quantum number $m$, which is…