A Brownian Particle and Fields I: Construction of Kinematics and Dynamics

TL;DR

This paper extends Nelson's stochastic quantum dynamics to a relativistic scalar electron, aiming to clarify the mechanism of field generation from a stochastic particle and improve the understanding of quantum trajectories.

Contribution

It introduces a novel extension of Nelson's framework to relativistic particles, linking stochastic motion with field generation in quantum field theory.

Findings

Proposes a relativistic stochastic model for scalar electrons

Connects stochastic particle motion with field creation mechanisms

Enhances the interpretation of quantum trajectories in relativistic contexts

Abstract

Tracking a real trajectory of a quantum particle still has been treated as the interpretation problem. It shall be expressed by a Brownian (stochastic) motion suggested by E. Nelson, however, the well-defined mechanism of field generation from a stochastic particle hasn't been proposed yet. For the improvement of this, I propose the extension of Nelson's quantum dynamics, for describing a relativistic scalar electron with its radiation equivalent to the Klein-Gordon particle and field system.