# Memory and the Infrared

## TL;DR

This paper explores how memory effects in scattering processes relate to asymptotic fields, soft theorems, and infrared-safe observables, proposing new conservation laws and a framework for detecting memory through radiated energy.

## Contribution

It introduces a novel set of conservation laws for scattering that are linked to soft modes and proposes a method to observe memory effects via infrared-safe cross sections.

## Key findings

- Memory effects are fully characterized by asymptotic retarded fields.
- New conservation laws are derived from zero radiated energy conditions.
- Infrared-safe cross sections depend only on scattering data and radiated energy.

## Abstract

Memory effects in scattering processes are described in terms of the asymptotic retarded fields. These fields are completely determined by the scattering data and the zero mode part is set by the soft photon theorem. The dressed asymptotic states defining an infrared finite S- matrix for charged particles can be defined as quantum coherent states using the corpuscular resolution of the asymptotic retarded fields. Im- posing that the net radiated energy in the scattering is zero leads to the new set of conservation laws for the scattering S-matrix which are equivalent to the decoupling of the soft modes. The actual observabil- ity of the memory requires a non vanishing radiated energy and could be described using the infrared part of the differential cross section that only depends on the scattering data and the radiated energy. This is the IR safe cross section with any number of emitted pho- tons carrying total energy equal to the energy involved in the actual memory detection.