The gauge-invariant dynamic equations for current-carrying plasma-like media with topological defects

Abstract

A closed set of the gauge-invariant dynamic equations for a current-carrying plasma- like medium with dislocation-type and disclination-type topological defects together with the conditions at strong discontinuities is obtained using the variational principle and discussed. The dislocation and disclination fields, which compensate the non-homogeneity of the action of the gauge group GD SO.3/FT. 3/, are described in the present theory by inexact external differential forms. The set of the Cartan structural equations for these forms has a direct correlation with the continuity equations for topological defects. The integrability conditions for the equations describing the dynamics of topological defects are obtained. It is shown that the integrability condition for the equation for disclination fields is equivalent to the balance equation for the angular momentum of the plasma-like medium together with the magnetic field. This condition is degenerated in the requirement of symmetry of the total stress tensor in the case of lack of topological defects. It is also shown that the total tensor of an energy-momentum of the plasma-like medium and of the magnetic field satisfies the balance equation.