Superstatistics approach to path integral for a relativistic particle

Abstract

Superstatistics permits the calculation of the Feynman propagator of a relativistic particle in a novel way from a superstatistical average over nonrelativistic single-particle paths. We illustrate this for the Klein-Gordon particle in the Feshbach-Villars representation, and for the Dirac particle in the Schr\"odinger-Dirac representation. As a by-product 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.