# Dressed states from gauge invariance

## TL;DR

This paper demonstrates that gauge invariance naturally leads to the correct dressed asymptotic states in QED, resolving previous issues and connecting dressed states with asymptotic symmetries.

## Contribution

It shows that imposing gauge invariance alone suffices to derive gauge-invariant dressed states, clarifying their relation to Gauss's law and asymptotic symmetries in QED.

## Key findings

- Gauge invariance determines dressed states without solving asymptotic Hamiltonian dynamics.
- Proper dressed states satisfy Gauss's law and are gauge invariant.
- The formalism links dressed states to asymptotic symmetries in QED.

## Abstract

The dressed state formalism enables us to define the infrared finite $S$-matrix for QED. In the formalism, asymptotic charged states are dressed by clouds of photons. The dressed asymptotic states are originally obtained by solving the dynamics of the asymptotic Hamiltonian in the far past or future region. However, there was an argument that the obtained dressed states are not gauge invariant. We resolve the problem by imposing a correct gauge invariant condition. We show that the dressed states can be obtained just by requiring the gauge invariance of asymptotic states. In other words, Gauss's law naturally leads to proper asymptotic states for the infrared finite $S$-matrix. We also discuss the relation between the dressed state formalism and the asymptotic symmetry for QED.