Stochastic Processes and the Dirac Equation with External Fields

TL;DR

This paper explores the connection between stochastic processes of classical particles and the Dirac equation with external fields, analyzing how asymmetric turning probabilities influence particle motion in 1+1 dimensions.

Contribution

It introduces a novel link between stochastic classical particle models and the Dirac equation, considering asymmetric turning probabilities in time.

Findings

Different turning probabilities affect particle trajectories.

The stochastic model reproduces features of the Dirac equation.

Insights into classical-quantum correspondence in external fields.

Abstract

The equation describing the stochastic motion of a classical particle in 1+1-dimensional space-time is connected to the Dirac equation with external gauge fields. The effects of assigning different turning probabilities to the forward and the backward moving particles in time are discussed.