Related papers: A note on the short-time quantum propagator
The Feynman propagator used in the conventional in-out formalism in quantum field theory is not a causal propagator as wave packets are propagated virtually instantaneously outside the causal region of the initial state. We formulate a…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
We consider classical and quantum propagators for two different time intervals. If these propagators follow one another in a Fibonacci sequence we get a discrete quasiperiodic system. A theorem due to Nielsen provides a novel conserved…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
A generalized canonical formulation of the theory of the electromagnetic Fokker interaction for a system of two particles is proposed. The functional integral on the generalized phase space is defined as the initial one in quantum theory.…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…
Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour…
We begin by giving correct expressions for the short-time action; following the work of one of us and Makri--Miller. We use these estimates to derive a correct expression modulo modulo delta(t)sqr for the quantum propagator and we show that…
The analogy between dynamics and optics had a great influence on the development of the foundations of classical and quantum mechanics. We take this analogy one step further and investigate the validity of Fermat's principle in…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
The classical notions of continuity and mechanical causality are left in order to refor- mulate the Quantum Theory starting from two principles: I) the intrinsic randomness of quantum process at microphysical level, II) the projective…
Quantized systems whose underlying classical dynamics possess an elaborate mixture of regular and chaotic motion can exhibit rather subtle long-time quantum transport phenomena. In a short wavelength regime where semiclassical theories are…
We develop a theory of Feynman propagators for the massive Klein--Gordon equation with asymptotically static perturbations. Building on our previous work on the causal propagators, we employ a framework based on propagation of singularities…
We obtained the Feynman propagators for a noncommutative (NC) quantum mechanics defined in the recently developed Doplicher-Fredenhagen-Roberts-Amorim (DFRA) NC background that can be considered as an alternative framework for the NC…
We demonstrate the existence of a complex Hilbert Space with Hermitian operators for calculations in \textit{classical} electromagnetism that parallels the Hilbert Space of quantum mechanics. The axioms of this classical theory are the…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…