The Birman-Krein formula for differential forms and electromagnetic scattering
Spectral Theory
2022-05-27 v3 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
We consider scattering theory of the Laplace Beltrami operator on differential forms on a Riemannian manifold that is Euclidean near infinity. Allowing for compact boundaries of low regularity we prove a Birman-Krein formula on the space of co-closed differential forms. In the case of dimension three this reduces to a Birman-Krein formula in Maxwell scattering.
Keywords
Cite
@article{arxiv.2104.13589,
title = {The Birman-Krein formula for differential forms and electromagnetic scattering},
author = {Alexander Strohmaier and Alden Waters},
journal= {arXiv preprint arXiv:2104.13589},
year = {2022}
}
Comments
22 pages, LaTeX, some typos corrected and more details and references added, restructured