Mechanics of Cosserat media: II. relativistic theory

TL;DR

This paper extends the non-relativistic Cosserat media theory to relativistic contexts using the Poincaré group, with examples including the Dirac electron and Weyssenhoff fluid, advancing the understanding of relativistic continuum mechanics.

Contribution

It introduces a relativistic formulation of Cosserat media based on the Poincaré group, expanding the theoretical framework from Euclidean to Minkowski space.

Findings

Relativistic Cosserat equations derived from Poincaré group

Application to Dirac electron as a Cosserat medium

Modeling of Weyssenhoff fluid in relativistic setting

Abstract

The derivation of the non-relativistic Cosserat equations that was described in Part I of this series of papers is extended from the group of rigid motions in three-dimensional Euclidian space to the Poincar\'e group of four-dimensional Minkowski space. Examples of relativistic Cosserat media are then given in the form of the free Dirac electron and the Weyssenhoff fluid.