On the Higgs mechanism and stress functions in the translational gauge theory of dislocations

In this Letter we discuss the Higgs mechanism in the linear and static translational gauge theory of dislocations. We investigate the role of the Nambu–Goldstone field and the Proca field in the dislocation gauge theory. In addition, we give the constitutive relations for (homogeneous) anisotropic, hemitropic and isotropic materials and also stress function tensors for the gauge theory of dislocations.