Contact interactions between particle worldlines

TL;DR

This paper develops a framework for contact interactions between point particles using worldline methods, connecting classical electrostatics with quantum field theory and exploring interactions at the level of worldline intersections.

Contribution

It introduces a novel approach to model particle interactions via worldline intersections, linking classical electrostatics and quantum field theory in a unified formalism.

Findings

Relates worldline path integrals to classical electrostatics.

Constructs a quantum theory of intersecting worldlines.

Shows partition functions include endpoint propagator couplings.

Abstract

We construct contact interactions for bosonic and fermionic point particles. We first relate the resulting theories to classical electrostatics by taking functional averages over worldlines whose endpoints are fixed to charged particles. Counting those paths which pass through a space-time point $x^{\mu}$ gives the static electric field at that point, provided we take the limit where the length measured along the worldlines is large. We also investigate corrections to the classical field that arise beyond leading order in this limit before constructing a theory of point particles that interact when their worldlines intersect. We quantise this theory and show that the partition function contains propagator couplings between the endpoints of the particles before discussing how this is related to the worldline formalism of quantum field theory and general action at a distance theories.