Exploration of a SU(2) Electrodynamics Based on Lehnert’s Revised Quantum Electrodynamics

Abstract

Historically, electromagnetic theory was developed for situations described by the U(1) group. The dynamics equations describing the transformations and interrelationships of the force field are the well-known Maxwell equations, and the group algebra underlying these equations are U(1). There was a need to extend these equations to describe SU(2) situations and to derive equations whose underlying algebra is SU(2). In this paper, we will start with Terence W. Barrett’s SU(2) symmetric form of electrodynamics based on topological considerations. Meanwhile, in a series of papers Bo Lehnert proposed a novel and revised version of Quantum Electrodynamics (RQED) based on Proca equations. Therefore, we will write down a combination between Barrett’s SU(2) electrodynamics with Lehnert’s RQED. It is hoped that this paper may stimulate further investigations and experiments in particular for finding physics beyond Standard Model. This is a preliminary report, so it is far from being a complete description of SU(2) electrodynamics.