Maxwell's equations are universal for locally conserved quantities

Lucas Burns

doi:10.1007/s00006-019-0979-7

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arXiv · 1906.02675

Maxwell's equations are universal for locally conserved quantities

Lucas Burns

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Abstract

A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's equations. This holds true for any conserved quantity satisfying a continuity equation. It is obtained by means of a strong form of the Poincar\'e lemma presented here that states: Divergence-free multivector fields locally possess curl-free antiderivatives on flat manifolds. The above converse is an application of this lemma in the case of divergence-free vector fields in spacetime. We also provide conditions under which the result generalizes to curved manifolds.

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Lucas Burns. 2019-06-04. Maxwell's equations are universal for locally conserved quantities. https://doi.org/10.1007/s00006-019-0979-7

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