# Infrared Divergences in QED, Revisited

## TL;DR

This paper revisits infrared divergences in QED, demonstrating that accounting for vacuum degeneracy and transitions yields finite, nonzero scattering amplitudes, providing a reinterpretation of the Faddeev-Kulish approach.

## Contribution

It shows that incorporating vacuum degeneracy and transitions in QED calculations results in infrared finite, nonzero amplitudes, revisiting and extending the Faddeev-Kulish framework.

## Key findings

- Conventional QED amplitudes vanish due to infrared divergences.
- Properly accounting for vacuum transitions yields finite, nonzero amplitudes.
- The approach reinterprets the Faddeev-Kulish construction mathematically and physically.

## Abstract

Recently it has been shown that the vacuum state in QED is infinitely degenerate. Moreover a transition among the degenerate vacua is induced in any nontrivial scattering process and determined from the associated soft factor. Conventional computations of scattering amplitudes in QED do not account for this vacuum degeneracy and therefore always give zero. This vanishing of all conventional QED amplitudes is usually attributed to infrared divergences. Here we show that if these vacuum transitions are properly accounted for, the resulting amplitudes are nonzero and infrared finite. Our construction of finite amplitudes is mathematically equivalent to, and amounts to a physical reinterpretation of, the 1970 construction of Faddeev and Kulish.