Conservation laws for the Maxwell-Dirac equations with a dual Ohm's law

TL;DR

This paper derives new conservation laws for Maxwell-Dirac equations incorporating dual Ohm's law, revealing non-local in time conservation properties in a linear conductivity framework.

Contribution

It applies Ibragimov's theorem to establish conservation laws for symmetrized Maxwell-Dirac equations with dual Ohm's law, highlighting non-local conservation laws.

Findings

Conservation laws are derived for the system with dual Ohm's law.

The system admits non-local in time conservation laws.

The approach generalizes previous results to include magnetic charges.

Abstract

Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov, we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and magnetic charges obey linear conductivity laws (dual Ohm's law). We find that this linear system allows for conservation laws which are non-local in time.