# Curing velocity superselection in non-relativistic QED by restriction to a lightcone

## TL;DR

This paper demonstrates that restricting electron states to the future lightcone in non-relativistic QED resolves velocity superselection, addressing a key aspect of the infrared problem and supporting the Buchholz-Roberts approach.

## Contribution

It shows that velocity superselection can be resolved in non-relativistic QED models by focusing on the algebra of fields localized in the future lightcone, linking to a broader equivalence of GNS representations.

## Key findings

- Velocity superselection is resolved by lightcone restriction.
- Equivalence of GNS representations for coherent states is established.
- Supports the Buchholz-Roberts approach to infrared issues.

## Abstract

It is physically expected that plane-wave configurations of the electron in QED induce disjoint representations of the algebra of the electromagnetic fields. This phenomenon of velocity superselection, which is one aspect of the infrared problem, is mathematically well established in non-relativistic (Pauli-Fierz type) models of QED. We show that velocity superselection can be resolved in such models by restricting the electron states to the subalgebra of the fields localized in the future lightcone. This actually follows from a more general statement about equivalence of GNS representations for coherent states of the algebra of the future lightcone in free electromagnetism. Our analysis turns out to be meaningful in the non-relativistic setting and provides evidence in favour of the Buchholz-Roberts approach to infrared problems.