Spacelike localization of long-range fields in a model of asymptotic electrodynamics

TL;DR

This paper investigates the localization properties of asymptotic electromagnetic fields in quantum electrodynamics, showing limitations for charged fields and proposing bi-localized observables through dressed fermion fields.

Contribution

It formulates a net of asymptotic field algebras with unbounded spacelike regions and demonstrates bi-localization of certain dressed fermion observables.

Findings

Electromagnetic fields can be localized in symmetrical spacelike cones.

Charged fields cannot be localized in such cones due to their tails.

Dressed fermion fields produce bi-localized observables.

Abstract

A previously proposed algebra of asymptotic fields in quantum electrodynamics is formulated as a net of algebras localized in regions which in general have unbounded spacelike extension. Electromagnetic fields may be localized in `symmetrical spacelike cones', but there are strong indications this is not possible in the present model for charged fields, which have tails extending in all space directions. Nevertheless, products of appropriately `dressed' fermion fields (with compensating charges) yield bi-localized observables.