# On string-localized potentials and gauge fields

## TL;DR

The paper examines a recent proposal to replace point-localized gauge fields with string-localized potentials in quantum field theory, showing limitations in describing gauge interactions and Gauss' law.

## Contribution

It demonstrates that string-localized potentials cannot fully replace gauge fields for describing gauge bridges in charged field interactions.

## Key findings

- String-localized potentials cannot describe gauge bridges between charged fields.
- These potentials do not suffice for the full description of gauge interactions in QED.
- The approach does not preclude Poincaré invariant theories with string-localized potentials.

## Abstract

A recent idea, put forward by Mund, Rehren and Schroer, is discussed; it suggests that in gauge quantum field theory one can replace the point-localized gauge fields by string-localized vector potentials built from gauge invariant observables and a principle of string-independence. Based on a kinematical model, describing unmovable (static) fields carrying opposite charges, it is shown that these string-localized potentials cannot be used for the description of the gauge bridges between electrically charged fields. These bridges are needed in order to ensure the validity of Gauss' law. This observation does not preclude the existence of Poincar\'e invariant theories, describing the coupling of string-localized gauge invariant potentials to matter fields. But these potentials are not a full-fledged substitute for the gauge fields in ``usual'' quantum electrodynamics.