Gauge Theory of Oriented Media

TL;DR

This paper introduces a gauge-theoretical framework for modeling oriented media using tensor wave fields, deriving gauge-invariant equations that describe the internal degrees of freedom in continua.

Contribution

It presents a novel gauge-theoretical approach to continuum media with internal orientations, deriving invariant equations from a variational principle.

Findings

Wave field as a tensor of second rank representing orientations

Derivation of gauge-invariant equations for oriented media

Establishment of a natural gauge group in continua

Abstract

The concept of wave field is introduced to represent oriented media. The wave field is a tensor field of second rank, and directors are its eigenvectors. This exhibition of directors defines a natural gauge group inherit in continua and allows one to derive from variational principle general relativistic and gauge invariant equations for the wave field in question. Thus, the gauge-theoretical approach to continuum with internal degrees of freedom gives unambiguous and minimally coupled theory.