Electrodynamics with quaternionic mass

TL;DR

This paper introduces a novel electrodynamics framework incorporating quaternionic mass, leading to new field equations, gauge invariance, and connections to axion and Proca theories, with implications for charge and current induction.

Contribution

It develops a quaternionic mass-based electrodynamics, deriving new Maxwell-Proca equations, and linking axion electrodynamics to Proca theory with gauge invariance.

Findings

Magnetic fields induce electric charge and current densities due to quaternionic mass.

Derived gauge-invariant Maxwell-Proca equations with quaternionic mass.

Established equivalence between axion and Proca electrodynamics.

Abstract

New electrodynamics with quaternionic mass is found to yields interesting results. The quaternionic mass involves longitudinal as well as transverse (vector) masses. Because of these two masses, an application of a magnetic field in a system induces electric charge and current densities in the system. Frank Wilczek axion electrodynamics is derived from this new electrodynamics bearing a quantum signature. A new version of Maxwell-Proca equations that are invariant under the gauge transformations is derived from the new electrodynamics. New electric and magnetic fields that are different from the standard formalism are proposed to describe massive electrodynamics. Axion electrodynamics are shown to be equivalent to Proca electrodynamics. The energy and momentum conservation equations are not influenced by the quaternionic mass.