Asymmetric total stress tensor

Abstract

From arguments based on momentum conservation, the stress boundary condition, the allowed functional dependence of a stress tensor, the gauge invariance, and the vacuum form of the Maxwell stress tensor, a proper identification of the total stress (or momentum flow) tensor for a closed system consisting of an arbitrary dielectric crystal in interaction with the electromagnetic field is found. This tensor is shown to be asymmetric even though the system conserves angular momentum. Jump conditions on the total stress tensor are found both for surfaces fixed in the spatial or laboratory coordinate system, and for surfaces fixed in the material or body coordinate system, and thus moving and deforming with respect to the laboratory coordinate system. The ideas developed are also applied to the flow of energy and the flow of angular momentum.