Note on soft theorems and memories in even dimensions

TL;DR

Addressing the link between soft theorems and memory effects in even spacetime dimensions, the paper develops a general framework in which soft factors are Fourier-transformed into radiation fields derived from classical field equations. It demonstrates that the radiation fields reproduce the soft-theorem structures for scalar, electromagnetic, and linearized gravitational theories, thus viewing classical results as limits of quantum amplitudes. In four dimensions memory effects appear as leading-order momentum kicks along null directions, while in higher even dimensions the leading memory is absent and nontrivial memory arises only at subleading orders, with explicit expressions in $d=6$ and $d=8$. The work clarifies how memory is encoded in radiation fields and discusses connections to asymptotic symmetries and potential observational implications in higher dimensions.

Abstract

Recently, it has been shown that the Weinberg's formula for soft graviton production is essentially a Fourier transformation of the formula for gravitational memory which provides an effective way to understand how the classical calculation arises as a limiting case of the quantum result. In this note, we propose a general framework that connects the soft theorems to the radiation fields obtained from classical computation for different theories in even dimensions. We show that the latter is nothing but Fourier transformation of the former. The memory formulas can be derived from radiation fields explicitly.