Symmetry Principles and Group Theory in Electromagnetics

TL;DR

This paper advocates for the integration of group theory into electromagnetics education, highlighting its benefits for understanding electromagnetic phenomena and reducing computational complexity.

Contribution

It provides a didactic overview of symmetry types and group representations in electromagnetics, emphasizing their pedagogical and practical advantages.

Findings

Enhanced physical understanding of electromagnetic phenomena

Reduction in numerical calculation complexity

Promotion of group theory as a fundamental tool in electromagnetics

Abstract

Group theory is used in many textbooks of contemporary physics. However, electromagnetic community often considers group theory as an "exotic" tool. Graduate and postgraduate textbooks on electromagnetics and electrodynamics usually do not contain a description of properties of electromagnetic fields and waves on the basis of group theory. We discuss in this paper from the didactic point of view, several types of symmetry and the corresponding groups and representations. The benefits of the use of group theoretical methods are a more deep physical understanding of the electromagnetic phenomena and a significant reduction of numerical calculations. These methods are general and exact.