Evolutionary equations and constraints: Maxwell equations
Abstract
By fixing a reference frame in spacetime, it is possible to split the EulerLagrange equations associated with a degenerate Lagrangian into purely evolutionary equations and constraints on the allowed Cauchy data with respect to the notion of Space and Time associated with the given reference frame. In the context of Classical Electrodynamics, we introduce a "covariantization procedure" that allows to invert the perspective and to recover a fullfledged covariant formulation of Maxwell's equations starting only with constraint equations (i.e., Gauss' law and the local version of the law of conservation of magnetic flux) as perceived in a sufficient number of (inertial) reference frames on Minkowski spacetime.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 November 2019
 DOI:
 10.1063/1.5109087
 arXiv:
 arXiv:1910.09654
 Bibcode:
 2019JMP....60k3503C
 Keywords:

 Mathematical Physics
 EPrint:
 Journal of Mathematical Physics, Volume 60, Issue 11, 2019