A gauge theoretic approach to elasticity with microrotations

TL;DR

This paper develops a gauge theoretic framework for elasticity incorporating microrotations, revealing particle-like soliton solutions with topological origins, inspired by concepts from gravitation and cosmology.

Contribution

It introduces a novel gauge theory formulation of elasticity with microrotations, demonstrating the existence of topological soliton solutions analogous to Skyrmions and Kinks.

Findings

Existence of particle-like solutions in the gauge theory model.

Equations of motion are of Sine-Gordon type, allowing soliton solutions.

Solutions have a topological origin similar to Skyrmions and Kinks.

Abstract

We formulate elasticity theory with microrotations using the framework of gauge theories, which has been developed and successfully applied in various areas of gravitation and cosmology. Following this approach, we demonstrate the existence of particle-like solutions. Mathematically this is due to the fact that our equations of motion are of Sine-Gordon type and thus have soliton type solutions. Similar to Skyrmions and Kinks in classical field theory, we can show explicitly that these solutions have a topological origin.