Note on soft theorems and memories in even dimensions

TL;DR

This paper establishes a general framework linking soft theorems to classical radiation fields in even dimensions, showing that memory effects are Fourier transforms of soft theorems, thus unifying quantum and classical perspectives.

Contribution

It introduces a unified framework connecting soft theorems with classical radiation fields in even dimensions, demonstrating their Fourier transform relationship.

Findings

Soft theorems are Fourier transforms of classical radiation fields.

Memory formulas can be explicitly derived from radiation fields.

The framework applies to various theories in even 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.