# $U(1)$ gauge symmetry free of redundancy and a generalized Byers-Yang theorem

## TL;DR

This paper reformulates $U(1)$ gauge theory to remove gauge redundancy using a local field interaction approach, preserving physical properties and generalizing the Byers-Yang theorem to open systems.

## Contribution

It introduces a redundancy-free $U(1)$ gauge formulation based on local interactions, extending the Byers-Yang theorem to open quantum systems.

## Key findings

- Redundancy in $U(1)$ gauge theory can be eliminated without losing physical properties.
- The reformulation preserves the invariance of the equations of motion.
- A generalized Byers-Yang theorem applicable to open systems is established.

## Abstract

We present a reformulation of the $U(1)$ gauge theory by eliminating the redundancy inherent in the conventional approach. Our reformulation is constructed on the basis of local field interaction approach to electrodynamics. The gauge symmetry in our framework is associated with a physical transformation, which represents the invariance of the equation of motion of a charged scalar field under the change in the distribution of electromagnetic field at a distance. We demonstrate that all physical properties of the $U(1)$ gauge theory are preserved with the removal of redundancy in the gauge field. In addition, our reformulation provides a generalization of the Byers-Yang theorem to open systems.