Path Integral for Relativistic Equations of Motion

TL;DR

This paper introduces a non-Grassmanian path integral approach for solving relativistic quantum equations, making trajectories differentiable through relativistic corrections and discussing the nonrelativistic limit via renormalization group analysis.

Contribution

It presents a novel path integral formulation for Klein-Gordon and Dirac equations that avoids Grassman variables and incorporates relativistic corrections.

Findings

Trajectories become differentiable with relativistic corrections.

The nonrelativistic limit is analyzed using renormalization group methods.

Provides a new perspective on relativistic quantum equations.

Abstract

A non-Grassmanian path integral representation is given for the solution of the Klein-Gordon and the Dirac equations. The trajectories of the path integral are rendered differentiable by the relativistic corrections. The nonrelativistic limit is briefly discussed from the point of view of the renormalization group.