On the fundamentals of the three-dimensional translation gauge theory of dislocations

TL;DR

This paper develops a dynamic three-dimensional gauge theory of dislocations, formulating field equations akin to Maxwell's theory, to better understand dislocation dynamics in materials.

Contribution

It introduces a dynamic gauge theory framework for dislocations, incorporating dislocation density and current tensors, and derives equations of motion in a Maxwell-like form.

Findings

Derived a closed system of field equations for dislocations.

Formulated a dynamical Peach-Koehler force density.

Highlighted similarities and differences with Maxwell field theory.

Abstract

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