Evolutionary equations and constraints: Maxwell equations

By fixing a reference frame in spacetime, it is possible to split the Euler-Lagrange 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 us to invert the perspective and to recover a full-fledged 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

Evolutionary equations and constraints: Maxwell equations Articles