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

TL;DR

This paper explores the application of the Higgs mechanism within the translational gauge theory of dislocations, analyzing the roles of Nambu-Goldstone and Proca fields, and providing constitutive relations and stress functions for various materials.

Contribution

It introduces a detailed analysis of the Higgs mechanism in dislocation gauge theory and derives constitutive relations and stress functions for different material symmetries.

Findings

Identification of the Higgs mechanism's role in dislocation gauge theory

Derivation of constitutive relations for anisotropic and isotropic materials

Development of stress function tensors for the gauge theory of dislocations

Abstract

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.