A dynamic version of the three-dimensional translation gauge theory of dislocations was proposed. In this approach, the notions of dislocation density and dislocation current tensors were used as the translational field strengths and corresponding response quantities (pseudomoment stress and dislocation momentum flux) were defined. A closed system of field equations was derived in an elegant quasi-Maxwellian form for the equations of motion of dislocations. The dynamical Peach-Koehler force density was also derived within this framework. The similarities and differences between Maxwell field theory and the dislocation gauge theory developed here were considered.

On the Fundamentals of the Three-dimensional Translation Gauge Theory of Dislocations. M.Lazar: Mathematics and Mechanics of Solids, 2011, 6[3], 253-64