A String Motivated Approach to the Relativistic Point Particle

TL;DR

This paper extends string theory-inspired methods to relativistic point particles, deriving a partition function for closed world lines and demonstrating its equivalence to traditional actions, with applications to effective Lagrangians.

Contribution

It introduces a string-motivated approach to relativistic particles, including closed world lines, and connects it to established formalisms with novel calculations.

Findings

Derived a partition function for closed world lines

Verified equivalence with the path length action

Computed the Euler-Heisenberg effective Lagrangian using the new approach

Abstract

Using concepts developed in string theory, Cohen, Moore, Nelson and Polchinski calculated the propagator for a relativistic point particle. Following these authors we extend the technique to include the case of closed world lines. The partition function found corresponds to the Feynmann and Schwinger proper time formalism. We also explicitly verify that the partition function is equivalent to the usual path length action partition function. As an example of a sum over closed world lines, we compute the Euler-Heisenberg effective Lagrangian in a novel way.