Ponderomotive forces in electrodynamics of moving media: The Minkowski   and Abraham approaches
  In the general setting of the problem, the explicit compact formulae are derived for the ponderomotive forces in the macroscopic electrodynamics of moving media in the Minkowski and Abraham approaches. Taking account of the Minkowski constitutive equations and making use of a special representation for the Abraham energy-momentum tensor enable one to obtain a compact expression for the Abraham force in the case of arbitrary dependence of the medium velocity on spatial coordinates and the time and for nonstationary external electromagnetic field. We term the difference between the ponderomotive forces in the Abraham and Minkowski approaches as the Abraham force not only under consideration of media at rest but also in the case of moving media. The Lorentz force is found which is exerted by external electromagnetic field on the conduction current in a medium, the covariant Ohm law and the constitutive Minkowski relations being taken into account. The physical argumentation is traced for definition of the 4-vector of the ponderomotive force as the 4-divergence of the energy-momentum tensor of electromagnetic field in a medium. 
V.V. Nesterenko and A.V. Nesterenko
physics.class-ph cond-mat.mes-hall math-ph math.MP