Large Gauge Effects and the Structure of Amplitudes

TL;DR

This paper demonstrates that large gauge transformations influence momentum conservation, leading to non-zero three-point amplitudes and resolving discrepancies between perturbative and exact field theory methods, with implications for gravitational scattering.

Contribution

It introduces the role of large gauge effects in modifying amplitude structures and provides a modified LSZ prescription to incorporate these effects in perturbative calculations.

Findings

Large gauge transformations alter momentum conservation.

Perturbative amplitudes are incomplete without large gauge effects.

Modified LSZ prescription recovers full non-perturbative results.

Abstract

We show that large gauge transformations modify the structure of momentum conservation leading to non-vanishing three-point amplitudes in a simple toy model of a gravitational wave event. This phenomenon resolves an apparent tension between perturbative scattering amplitude computations and exact methods in field theory. The tension is resolved to all orders of perturbation theory once large gauge effects are included via a modified LSZ prescription; if they are omitted, perturbative methods only recover a subset of terms in the full non-perturbative expression. Although our results are derived in the context of specific examples, several aspects of our work have analogues in dynamical gravitational scattering processes.