Line geometry and electromagnetism II: wave motion

TL;DR

This paper explores the application of line geometry to wave motion, focusing on electromagnetic waves and their dispersion laws derived from constitutive relations and field equations.

Contribution

It introduces a geometric framework using line complexes to analyze electromagnetic wave propagation and dispersion laws.

Findings

Line geometry provides a useful perspective on wave surfaces.

Dispersion laws are derived from constitutive laws via geometric methods.

The approach links geometric concepts with electromagnetic wave theory.

Abstract

The fundamental role of line geometry in the study of wave motion is first introduced in the general context by way of the tangent planes to the instantaneous wave surfaces, in which it is first observed that the possible frequency-wave number 1-forms are typically constrained by a dispersion law that is derived from a constitutive law by way of the field equations. After a general review of the basic concepts that relate to quadratic line complexes, these geometric notions are applied to the study of electromagnetic waves, in particular.