Related papers: Hilbert Space Theory of Classical Electrodynamics
Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schr\"odinger…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
Quantum mechanical time operator is introduced following the parametric formulation of classical mechanics in the extended phase space. Quantum constraint on the extended quantum system is defined in analogy to the constraint of the…
We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the…
We present three statistical descriptions for systems of classical particles and consider their extension to hybrid quantum-classical systems. The classical descriptions are ensembles on configuration space, ensembles on phase space, and a…
Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert…
Using quantum-classical analogies, we find that dynamical pictures of quantum mechanics have precise counterparts in classical mechanics. In particular, the Eulerian and Lagrangian descriptions of fluid dynamics in classical mechanics are…
Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely Glauber and SU(2) coherent…
We consider a non-relativistic particle in a one-dimensional box with all possible quantum boundary conditions that make the kinetic-energy operator selfadjoint. We determine the Wigner functions of the corresponding eigenfunctions and…
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…
Classically, electromagnetic pulses are described by real fields that couple to charged matter and propagate causally. We will show here that real fields of the form used in standard classical electromagnetic theory have a quantum…
We propose a novel semiclassical mechanism to unify quantum mechanics and general relativity, where wave function collapse in a superposition state induces a rapid change in the energy-momentum tensor, triggering spacetime dynamics that…
Bohmian mechanics, a hydrodynamic formulation of quantum mechanics, relies on the concept of trajectory, which evolves in time in compliance with dynamical information conveyed by the wave function. Here this appealing idea is considered to…
Based on Koopman's theory of classical wavefunctions in phase space, we present the Koopman-van Hove (KvH) formulation of classical mechanics as well as some of its properties. In particular, we show how the associated classical Liouville…
We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance, which are often used as toy models of quantum gravity. The first approach is based on the…
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
A manifestly gauge-invariant hamiltonian formulation of classical electrodynamics has been shown to be relativistic invariant by the construction of the adequate generators of the Poincare Lie algebra [Physica, 76, No. 3, 421-444 (1974)].…
The manipulation of mechanical waves is a long-standing challenge for scientists and engineers, as numerous devices require their control. The current forefront of research in the control of classical waves has emerged from a seemingly…
Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space,…
We propose a new relativistic Lorentz-invariant spin-noncommutative algebra. Using the Weyl ordering of noncommutative position operators, we build an analogue of the Moyal-Groenewald product for the proposed algebra. The Lagrange function…