Relativistic Elastomechanics is a Gauge--Type Theory

TL;DR

This paper introduces a novel gauge--type formulation of relativistic elasticity, where material space diffeomorphisms act as gauge transformations, leading to a set of hyperbolic PDEs describing elastic dynamics.

Contribution

It presents a new gauge--theoretic framework for relativistic elasticity, connecting it with gauge theories and extending previous approaches.

Findings

Formulation of elastic dynamics as hyperbolic PDEs

Establishment of gauge symmetry in relativistic elasticity

Discussion of relation to Carter-Quintana approach

Abstract

A new approach to relativistic elasticity theory is proposed. In this approach the theory becomes a gauge--type theory, with the diffeomorphisms of the material space playing the role of gauge transformations. The dynamics of the elastic material is expressed in terms of three independent, hyperbolic, second order partial differential equations imposed on three (independent) gauge potentials. The relationship with the Carter-Quintana approach is discussed.