Time symmetric electrodynamics, electric charge conservation, and the Lorenz gauge

TL;DR

This paper explores the deep connection between the Lorenz gauge condition and electric charge conservation within time symmetric electrodynamics, using historical insights and path integral formulations in Minkowski space.

Contribution

It introduces a novel perspective linking gauge conditions and charge conservation through closed path integrals involving Wheeler electrons.

Findings

Lorenz gauge condition relates to charge conservation via path integrals.

Charge conservation and gauge condition are expressed as closed path integrals.

The approach relies on time symmetric electrodynamics and historical observations.

Abstract

We reveal a new way in which the Lorenz gauge condition is related to the electric charge conservation, in a universe where electrically charged point particles are created and annihilated. We derive our results using time symmetric electrodynamics, relying on observations made by Jacov Frenkel (in 1925) and John Archibald Wheeler (in 1940). Both the Lorenz gauge condition and the electric charge conservation are expressed as closed path integrals in Minkowski space. The integration path is the same, it is the sum of all "Wheeler electrons".