On the Fundamentals of the Three-dimensional Translation Gauge Theory of Dislocations

We propose a dynamical version of the three-dimensional translation gauge theory of dislocations. In our approach, we use the notions of dislocation density and dislocation current tensors as the translational field strengths and define corresponding response quantities (pseudomoment stress and dislocation momentum flux). For the equations of motion for dislocations, we derive a closed system of field equations in an elegant quasi-Maxwellian form. The dynamical Peach-Koehler force density is derived in this framework as well. Finally, we discuss the similarities and differences between Maxwell field theory and the dislocation gauge theory developed here.