On the gauge transformations admitted by the equations of defect dynamics

Abstract

This paper deals with gauge invariance applied to dislocations and disclinations in the field theory formulation given by Kossecka and de Wit[1,2]. The gauge transformations of the strain, linear velocity, bend-twist, and rotational velocity that leave the dislocation and disclination densities and currents invariant are obtained explicitly, and the equations of balance of linear momentum are shown to lead to a natural gauge condition. These transformations are generated by a vector field that depends upon position and time and two vector fields that depend on time alone. The latter two fields are shown to realize superimposed rigid body motions as part of the generalized gauge transformation structure of the theory. Representation of the space and time generating vector in terms of a gradient plus the curl of another vector is shown to lead to several useful decompositions.