Relativistic Lagrangian model of a nematic liquid crystal interacting with an electromagnetic field

TL;DR

This paper presents a relativistic Lagrangian framework for nematic liquid crystals interacting with electromagnetic fields, analyzing light propagation, deriving equations of motion, and addressing the Abraham-Minkowski momentum controversy.

Contribution

It introduces a comprehensive relativistic variational model for nematic liquid crystals coupled with electromagnetic fields, including explicit optical metrics and systematic derivation of energy-momentum tensors.

Findings

Explicit optical metrics for moving uniaxial media

Complete equations of motion for the coupled system

Insights into the Abraham-Minkowski momentum controversy

Abstract

We develop a relativistic variational model for a nematic liquid crystal interacting with an electro- magnetic field. The constitutive relation for a general anisotropic uniaxial diamagnetic and dielectric medium is analyzed. We discuss light wave propagation in this moving uniaxial medium, for which the corresponding optical metrics are identified explicitly. A Lagrangian for the coupled system of a nematic liquid crystal and the electromagnetic field is constructed, from which a complete set of equations of motion for the system is derived. The canonical energy-momentum and spin tensors are systematically obtained. We compare our results with those within the non-relativistic models. As an application of our general formalism, we discuss the so-called Abraham-Minkowski controversy on the momentum of light in a medium.