Classical and Quantum Interaction of the Dipole Revisited

TL;DR

This paper revisits the quantum and classical interactions of electric and magnetic dipoles with electromagnetic fields using 4D geometric quantities, revealing that previous relativistic assumptions about phase shifts are incorrect.

Contribution

It introduces new 4D commutation relations for dipole moments and angular momentum, and corrects the relativistic interpretation of quantum forces and phase shifts.

Findings

The 3D force expression is not relativistically correct.

Quantum 4-force is non-zero in proposed experiments.

Previous topological phase shift claims are invalid.

Abstract

The interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is investigated in an approach that deals with four-dimensional (4D) geometric quantities. The new commutation relations for the 4D orbital and intrinsic angular momentums and also for the 4D dipole moments are introduced. The expectation value of the quantum 4-force, which holds in any frame, is worked out in terms of them. In contrast to it the whole calculation in [1] ([1] J. Anandan, Phys. Rev. Lett. \textbf{85}, 1354 (2000)) has been made only in the rest frame of the dipole. It is proved that, e.g., the expression for the 3D force $\mathbf{f}%_{S}$ in [1] is not relativistically correct and that the quantum 4-force is not zero in the experiments proposed in [1]. This means that the phase shifts that could be observed in such experiments are not topological phase shifts.