Levy flights and nonlocal quantum dynamics

TL;DR

This paper develops a nonlocal quantum dynamics framework by generalizing the Schrödinger equation with pseudodifferential operators, analyzing wave packet evolution, and extending covariant particle equations to Maxwell theory, linking to photon wave mechanics.

Contribution

It introduces a nonlocal operator-based approach to quantum evolution, extending the Salpeter equation and covariant particle equations to encompass Maxwell theory and photon mechanics.

Findings

Generalized Schrödinger evolution with nonlocal operators.

Analyzed wave packet radial expansion in 3D.

Extended covariant particle equations to Maxwell theory.

Abstract

We develop a fully fledged theory of quantum dynamical patterns of behavior that are nonlocally induced. To this end we generalize the standard Laplacian-based framework of the Schr\"{o}dinger picture quantum evolution to that employing nonlocal (pseudodifferential) operators. Special attention is paid to the Salpeter (here, $m\geq 0$) quasirelativistic equation and the evolution of various wave packets, in particular to their radial expansion in 3D. Foldy's synthesis of "covariant particle equations" is extended to encompass free Maxwell theory, which however is devoid of any "particle" content. Links with the photon wave mechanics are explored.