String-localized Quantum Fields and Modular Localization

TL;DR

This paper investigates string-localized quantum fields, especially for massless infinite spin and massive representations, revealing their structure and relation to point-localized fields and gauge conditions.

Contribution

It introduces a framework for string-localized quantum fields associated with Poincaré group representations, including those incompatible with point-like localization.

Findings

String-localized fields for infinite spin representations are constructed.

Massive and finite helicity massless fields can be expressed as integrals of point-localized fields.

Relation between string-localized vector fields and axial gauge conditions is established.

Abstract

We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincar\'e group and localized in semi-infinite strings extending to spacelike infinity. Among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point-like localized fields. For the massive representation and the massless representations of finite helicity, all string-localized free fields can be written as an integral, along the string, of point-localized tensor or spinor fields. As a special case we discuss the string-localized vector fields associated with the point-like electromagnetic field and their relation to the axial gauge condition in the usual setting.