Gauge field theoretic solution of a uniformly moving screw dislocation and admissibility of supersonic speeds

The failure of classical elasticity to address dislocation behavior spatially close to its core and (in Lorentz-type fashion) near the speed of sound is well known. In gauge field theory of defects, the latter are not postulated a priori in an ad hoc fashion rather defects such as dislocations arise naturally as a consequence of broken translational symmetry exhibiting solutions that are physically meaningful (e.g., removal of divergence of stress and the natural emergence of a core making redundant the artificial cut-off radius). In the present work we present the gauge field theoretic solution to the problem of a uniformly moving screw dislocation. Apart from the formal derivations, we show that stress divergence at the core of the dislocation is removed at all time and (consistent with atomistic simulations), supersonic states are found to be admissible.