Symmetries of the equations of pre-metric electromagnetism

TL;DR

This paper analyzes the symmetries of pre-metric electromagnetism equations, revealing that their most physically relevant symmetry algebra is related to infinitesimal projective transformations in four-dimensional space.

Contribution

It formulates pre-metric electromagnetism as an exterior differential system and applies the Harrison-Estabrook method to identify its symmetry algebra.

Findings

The symmetry algebra is the Lie algebra of infinitesimal projective transformations.

Among four possible symmetry algebras, the most physically relevant is identified.

The formulation uses exterior differential systems on the bundle of 2-forms.

Abstract

The equations of pre-metric electromagnetism are summarized and then formulated as an exterior differential system on the total space of the bundle of 2-forms over the spacetime manifold. The Harrison-Estabrook method of computing the symmetries of the system is then applied, with the result that of the four possible formal algebras of infinitesimal symmetries, the most physically compelling one is the Lie algebra of infinitesimal projective transformations of real four-dimensional projective space.