Soft Theorems from Boundary Terms in the Classical Point Particle Currents

TL;DR

This paper demonstrates that boundary terms in classical point particle currents account for soft theorems at tree level, explaining their universality up to sub-leading orders and their factorization in scattering amplitudes.

Contribution

It identifies boundary terms in classical currents as the origin of soft theorems and clarifies their limitations beyond sub-leading orders.

Findings

Boundary terms in classical currents correspond to soft factors.

Universality of soft theorems holds only up to sub-leading orders.

Boundary terms factor out of tree-level amplitudes in scalar-graviton interactions.

Abstract

Soft factorization has been shown to hold to sub-leading order in QED and to sub-sub-leading order in perturbative quantum gravity, with various loop and non-universal corrections that can be found. Here we show that all terms factorizing at tree level can be uniquely identified as boundary terms that exist already in the classical expressions for the electric current and stress tensor of a point particle. Further, we show that one cannot uniquely identify such boundary terms beyond the sub-leading or sub-sub-leading orders respectively, providing evidence that the "universality" of the tree level soft factor only holds to these orders. Finally, we show that these boundary terms factor out of all tree level amplitudes as expected, in a theory where gravitons couple to a scalar field.