Related papers: A note on the short-time quantum propagator
Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…
It is shown that the complex phase of the Feynman propagator is a solution of the quantum Hamilton Jacobi equation
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…
We argue that quantum mechanics makes sense without such controversial postulates as the wave function collapse, the quantum probability rule and the observable postulate. We only need the existence of a wave function as a representation of…
It has long been recognized that the dynamics of linear quantum systems is classical in the Wigner representation. Yet many conceptually important linear problems are typically analyzed using such generally applicable techniques as…
In this work we study basic properties of unstable particles and scalar hadronic resonances, respectively, within simple quantum mechanical and quantum field theoretical (effective) models. We start with the basic ideas of quantum field…
We discuss the Heisenberg-Wigner phase-space formalism in quantum electrodynamics as well as scalar quantum electrodynamics with respect to transverse fields. In regard to the special characteristics of such field types we derive modified…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
The main aim of this note is to show that the formalism of multi-time equations in quantum mechanics meant to represent a manifestly Lorentz-invariant theory suffers from at least three imperfections: (1) It does not cover those physical…
The non-Hermitian quadratic oscillator studied by Swanson is one of the popular $PT$-symmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
The five laws of relativistic quantum mechanics, according to Feynman's path integral formulation, are concisely stated and applied to experiments. Reflection diffraction grating experiments for both photons and electrons are analysed, in…
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
We present critical arguments against individual interpretation of Bohr's complementarity and Heisenberg's uncertainty principles. Statistical interpretation of these principles is discussed in the contextual framework. We support the…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. (The theory is constructive in that, operators acting at different times, actually commute.) We first develop an operator version of the…
The propagation of the wave function of a particle is characterised by a group and a phase velocity. The group velocity is associated with the particle's classical velocity, which is always smaller than the speed of light, and the phase…
Typically the use of the Rayleigh-Sommerfeld diffraction formula as a photon propagator is widely accepted due to the abundant experimental evidence that suggests that it works. However, a direct link between the propagation of the…
It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with…