Conserved geometric phase and group velocity

TL;DR

This paper uses conserved geometric phase and group velocity concepts, combined with representation theory, to derive key physical quantities describing dielectric and magnetic responses in crystalline materials, including dipole moments and induced currents.

Contribution

It introduces a novel approach integrating geometric phase and group velocity with representation theory to derive physical response quantities in crystals.

Findings

Derived the macroscopic dipole moment per unit volume.

Expressed the current induced by a static external electromagnetic field.

Provided a theoretical framework connecting geometric phase with material responses.

Abstract

In this paper we make use of the concept of conserved geometric phase and of group velocity,in conjunction with the representation theory\cite{Dirac,Dirac-letture}, in order to derive some relevant physical quantities for the description of the dielectric and magnetic response of crystalline materials. As an application of the model, we derive the expression of the macroscopic dipole moment per unit volume, and the expression of the current induced by a uniform static external electromagnetic field.