Conserved geometric phase and group velocity

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.