Force law in material media and quantum phases

TL;DR

This paper derives a relativistically consistent force law for electric and magnetic dipoles, revealing two new quantum phases that occur when dipoles move in their respective fields, challenging previous models.

Contribution

It introduces a Lagrangian-based derivation of the force on small dipoles, predicting novel quantum phases not accounted for in earlier theories.

Findings

Identifies incompatibility of existing force expressions with relativistic transformations.

Predicts two new quantum phases for moving electric and magnetic dipoles.

Discusses implications for quantum and classical electromagnetic theory.

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, correspondingly. The implications of the obtained results are discussed.