Momentum, pseudomomentum, and wave momentum: Toward resolving the Minkowski-Abraham controversy

We derive the momentum and pseudomomentum conservation laws from a very general nonrelativistic Lagrangian theory of the interaction of the electromagnetic field with a deforming, dispersive dielectric. From the former of these laws, we obtain the momentum density of an electromagnetic wave in matter to be ${\mathrm{\epsilon }}_0$ E×B, not the Abraham form of ${\mathrm{\epsilon }}_0$ E×${\mathrm{\mu }}_0$ H. From the latter of these laws, we obtain the electromagnetic pseudomomentum density in the absence of deformation of the matter to be P×B plus a dispersive term, not the Minkowski form of D×B as proposed by Blount (unpublished). We show by quantizing the energy of the wave that the sum of momentum and pseudomomentum, which we name wave momentum, corresponds to Nħk (N an integer), the quantity that enters wave-vector conservation or phase-matching relations in wave interactions and that is consistent with the Jones-Richards experiment.