Topological aspects of zero modes in cavity resonators
Accelerator Physics
2026-01-27 v2 Classical Physics
Abstract
We discuss the relationship between the zero modes of electromagnetic fields in a cavity resonator and the cavity's topological characteristics. We show that the dimension of the electromagnetic zero-mode space coincides with the dimension of the corresponding homology group of the cavity. Moreover, we prove that the alternating sum of the dimensions of the electromagnetic zero-mode spaces is closely related to the Euler characteristic of the cavity boundary, and hence to the integral of the curvature.
Keywords
Cite
@article{arxiv.2601.11989,
title = {Topological aspects of zero modes in cavity resonators},
author = {Osamu Kamigaito},
journal= {arXiv preprint arXiv:2601.11989},
year = {2026}
}
Comments
17 pages, 1 figure. Diagram corrected