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 ε₀E×{}B, not the Abraham form of ε₀E×{}μ₀H. 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of deformation of the matter to be P×{}B plus a dispersive term, not the Minkowski form of D×{}B as proposed by Blount (unpublished).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 N{}k (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.