Force law in material media and quantum phases

Abstract

We show that the known expressions for the force on a point-like dipole are incompatible with the relativistic transformation of force, and in this respect we apply the Lagrangian approach to the derivation of the correct equation for force on a small electric/magnetic dipole. The obtained expression for the generalized momentum of a moving dipole predicts two novel quantum effects with non-topological and non-dynamic phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field, respectively.