# The stepwise path integral of the relativistic point particle

## TL;DR

This paper develops a stepwise geometric construction of the relativistic point particle's path integral in Euclidean space, resolving symmetry-related overcounting issues to accurately compute the quantum propagator.

## Contribution

It introduces a novel stepwise method for constructing the relativistic path integral that addresses symmetry overcounting and provides a geometric calculation of the propagator.

## Key findings

- Resolved the breakdown of the Chapman-Kolmogorov relation in the path integral
- Provided a geometric method for calculating the relativistic propagator
- Clarified the role of local and global symmetries in the path integral

## Abstract

In this paper we present a stepwise construction of the path integral over relativistic orbits in Euclidean spacetime. It is shown that the apparent problems of this path integral, like the breakdown of the naive Chapman-Kolmogorov relation, can be solved by a careful analysis of the overcounting associated with local and global symmetries. Based on this, the direct calculation of the quantum propagator of the relativistic point particle in the path integral formulation results from a simple and purely geometric construction. paperpitch https://www.youtube.com/watch?v=tNMbCgPbq2A