The Birman-Krein formula for differential forms and electromagnetic scattering

2021/04/28 by Alexander Strohmaier, Strohmaier, Alexander, Alden Waters +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2104.13589

openalex publication_date 2021/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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