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

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.