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

Gauge Field Theoretic Solution of a Uniformly Moving Screw Dislocation and Admissibility of Supersonic Speeds. P.Sharma, X.Zhang: Physics Letters A, 2006, 349[1-4], 170-6