Superstatistics approach to path integral for a relativistic particle

TL;DR

This paper introduces a superstatistics method to compute relativistic particle propagators by averaging over non-relativistic paths, offering new insights into the worldline representation and Lorentz group structure.

Contribution

It presents a novel superstatistics approach to derive relativistic propagators from non-relativistic path integrals, connecting to worldline and Lorentz group representations.

Findings

Reproduces Klein-Gordon and Dirac propagators via superstatistics

Provides a new perspective on reparametrization fixing

Introduces a novel Lorentz group representation for Feshbach-Villars particles

Abstract

Superstatistics permits the calculation of the Feynman propagator of a relativistic particle in a novel way from a superstatistical average over non-relativistic single-particle paths. We illustrate this for the Klein-Gordon particle in the Feshbach-Villars representation, and for the Dirac particle in the Schroedinger-Dirac representation. As a byproduct we recover the worldline representation of Klein-Gordon and Dirac propagators, and discuss the role of the smearing distributions in fixing the reparametrization freedom. The emergent relativity picture that follows from our approach together with a novel representation of the Lorentz group for the Feshbach-Villars particle are also discussed.