Dress code for infrared safe scattering in QED

TL;DR

This paper develops a framework for analyzing infrared-safe scattering in QED using dressed states, linking memory effects to asymptotic symmetries, and deriving a generalized soft photon theorem.

Contribution

It introduces an infrared factorization formula for dressed states, clarifies conditions for infrared safety, and extends the soft photon theorem to general dressed states.

Findings

Derived an infrared factorization formula for dressed states.

Identified the memory effect as a conservation law of asymptotic symmetry.

Computed inclusive cross-sections using dressed states, avoiding infrared divergence issues.

Abstract

We study the $S$-matrix and inclusive cross-section for general dressed states in quantum electrodynamics. We obtain an infrared factorization formula of the $S$-matrix elements for general dressed states. It enables us to study what dressed states lead to infrared-safe $S$-matrix elements. The condition for dressed states can be interpreted as the memory effect which is nothing but the conservation law of the asymptotic symmetry. We derive the generalized soft photon theorem for general dressed states. We also compute inclusive cross-section using general dressed states. It is necessary to use appropriate initial and final dressed states to evaluate interference effects, which cannot be computed correctly by using Fock states due to the infrared divergence.