Quantization Conditions and the Double Copy

TL;DR

This paper connects Wilson loop observables with scattering amplitudes to derive quantization conditions and their gravitational double copy, providing relativistic generalizations of known quantum phenomena.

Contribution

It introduces a novel formulation of Wilson loops in terms of scattering amplitudes and derives relativistic quantization conditions and phases for gravitational systems.

Findings

Derived Dirac-Schwinger-Zwanziger quantization condition from scattering amplitudes.

Established gravitational (Taub-NUT) double copy of the quantization condition.

Computed relativistic Wilson loop for anyon-anyon system, generalizing Aharonov-Bohm phase.

Abstract

We formulate Wilson loop observables as products of eikonal Wilson lines given in terms of on-shell scattering amplitudes. Using these, we derive the Dirac-Schwinger-Zwanziger quantization condition and its gravitational (Taub-NUT) double copy, where we find a relativistic generalisation of the usual non-relativistic gravitational quantization condition. We also compute the relativistic Wilson loop for an anyon-anyon system, obtaining a similar relativistic generalisation of the Aharonov-Bohm phase for gravitational anyons.