Covariant Formulation of the Dynamics in a Dissipative Dielectric Obtained from a Simplified Lagrangian

Equations of motions and energy-momentum density tensors are obtained for a dispersive and dissipative medium sustaining electric and magnetic polarizations, using Lagrangian formalisms. A previous work on the subject by the authors has been simplified by reduction in the Lagrangian of the number of independent vector fields, with which the sink modes (associated with the dissipation) interact. The paper also formulates the dynamics of the electromagnetic field in the medium in a covariant (relativistic) manner. We discuss (and compare) the results, especially from the point of view of the positivity of the energy density.