Resumen de Symmetries, Lagrangian and Conservation Laws for the Maxwell Equations
The evolution equations of Maxwell�s equations has a Lagrangian written in terms of the electric E and magnetic H fields, but admit neither Lorentz nor conformal transformations. The additional equations ??E=0, ??H=0 guarantee the Lorentz and conformal invariance, but the resulting system is overdetermined, and hence does not have a Lagrangian. The aim of the present paper is to attain a harmony between these two contradictory properties and provide a correspondence between symmetries and conservation laws using the Lagrangian for the evolutionary part of Maxwell�s equations.
