Maxwell's equations are universal for locally conserved quantities
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 Poincaré lemma presented here that states: Divergencefree multivector fields locally possess curlfree antiderivatives on flat manifolds. The above converse is an application of this lemma in the case of divergencefree vector fields in spacetime. We also provide conditions under which the result generalizes to curved manifolds.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.02675
 Bibcode:
 2019arXiv190602675B
 Keywords:

 Physics  Classical Physics;
 Mathematical Physics
 EPrint:
 doi:10.1007/s0000601909797