Fractional Quantum Field Theory, Path Integral, and Stochastic Differential Equation for Strongly Interacting Many-Particle Systems

TL;DR

This paper introduces a fractional quantum field theory framework for strongly interacting many-particle systems, linking fractional wave equations, path integrals, and stochastic differential equations to describe their complex dynamics.

Contribution

It develops a novel theoretical approach connecting fractional quantum fields with stochastic processes for strongly interacting particles.

Findings

Strongly interacting particles follow fractional wave equations.

Particle trajectories exhibit Lévy walk behavior.

The framework unifies path integral and stochastic differential equation descriptions.

Abstract

While free and weakly interacting particles are well described by a a second-quantized nonlinear Schr\"odinger field, or relativistic versions of it, the fields of strongly interacting particles are governed by effective actions, whose quadratic terms are extremized by fractional wave equations. Their particle orbits perform universal L\'evy walks rather than Gaussian random walks with perturbations.