Classical Double Copy of Worldline Quantum Field Theory

TL;DR

This paper extends worldline quantum field theory to include charged particles and establishes a classical double copy relation for gravitational and gauge interactions, confirming its consistency with quantum amplitude double copy at NLO.

Contribution

It introduces a double copy framework within WQFT for classical observables and demonstrates its agreement with quantum amplitude relations up to next-to-leading order.

Findings

Classical double copy relation established for WQFT observables.

Computed NLO eikonal scattering phase using double copy.

Confirmed equivalence of WQFT double copy with quantum amplitude double copy.

Abstract

The recently developed worldline quantum field theory (WQFT) formalism for the classical gravitational scattering of massive bodies is extended to massive, charged point particles coupling to bi-adjoint scalar field theory, Yang-Mills theory, and dilaton-gravity. We establish a classical double copy relation in these WQFTs for classical observables (deflection, radiation). The bi-adjoint scalar field theory fixes the locality structure of the double copy from Yang-Mills to dilaton-gravity. Using this the eikonal scattering phase (or free energy of the WQFT) is computed to next-to-leading order (NLO) in coupling constants using the double copy as well as directly finding full agreement. We clarify the relation of our approach to previous studies in the effective field theory formalism. Finally, the equivalence of the WQFT double copy to the double copy relation of the classical limit of quantum scattering amplitudes is shown explicitly up to NLO.