The non-Riemannian dislocated crystal: a tribute to Ekkehart Kr\"oner (1919-2000)

TL;DR

This paper honors Ekkehart Kr"oner's work on the non-Riemannian geometric modeling of crystals with defects, offering a new perspective on the theory and addressing open questions about its dynamical variables.

Contribution

It provides an expository review and a novel perspective on Kr"oner's non-Riemannian geometric theory of defective crystals, aiming to clarify the theory's dynamical variables.

Findings

Revisits Kr"oner's non-Riemannian geometry of crystals

Proposes a new interpretation of the theory's variables

Addresses the open question of the dynamical variables

Abstract

This expository paper is a tribute to Ekkehart Kr\"oner's results on the intrinsic non-Riemannian geometrical nature of a single crystal filled with point and/or line defects. A new perspective on this old theory is proposed, intended to contribute to the debate around the still open Kr\"oner's question: "what are the dynamical variables of our theory?"