Classical off-shell currents

TL;DR

This paper develops a method to construct classical off-shell currents involving massive particles and massless bosons, connecting them to the Worldline Quantum Field Theory framework and applications in classical physics.

Contribution

It introduces a novel approach to build off-shell currents using coherent wave-functions, linking them to WQFT and enabling classical limit applications.

Findings

Currents encode solutions to classical equations of motion.

Application to scalar, gauge, and gravitational theories.

Connection to classical scattering amplitudes and thermal loops.

Abstract

We consider tree-level off-shell currents of two massive particles and $n$ massless bosons in the classical limit, which can be fused into the classical limit of $n+2$ scattering amplitudes. We show that dressing up the current with coherent wave-functions associated with the massive particles leads to the recently proposed Worldline Quantum Field Theory (WQFT) path integral. The currents thus constructed encode solutions of classical equations of motion so they can be applied to contexts where the classical limit is relevant, including hard thermal loops. We give several examples of these currents in scalar, gauge and gravitational theories.