Physical implications of the use of primitive and traceless electric quadrupole moments

Abstract

Theories of certain electromagnetic effects, such as chiral phenomena in fluids and crystals and gyrotropic birefringence in antiferromagnetic crystals, require the inclusion of electric quadrupole contributions for a full description of the effect. In a number of these theories the electric quadrupole moment is defined to be traceless, as indeed is the general practice for such moments in nuclear physics. It is shown that, when the traceless quadrupole moment is used in the derivation of the wave equation that describes light propagation through an optically active uniaxial medium, this equation and properties derived from it, in particular refractive index, depend in general on the arbitrary origin used to specify the quadrupole moment. This is physically unacceptable for an observable property of a substance. By contrast, this defect does not occur if the definition of the primitive quadrupole moment is adopted, namely Σqr α r β.