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 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.
Journal of Mathematical Physics
- Pub Date:
- November 2019
- Mathematical Physics
- Journal of Mathematical Physics, Volume 60, Issue 11, 2019