Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions

2022/11/18 by Badreddine Benhellal, Benhellal, Badreddine, Konstantin Pankrashkin +1
Mathematics · #35Q40 (Primary) 47A10 #58J40 (Secondary) #Advanced Operator Algebra Research #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2211.10264

openalex publication_date 2022/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the spectral properties of three-dimensional Dirac operators with critical combinations of electrostatic and Lorentz scalar shell interactions supported by a compact smooth surface. It turns out that the criticality of the interaction may result in a new interval of essential spectrum. The position and the length of the interval are explicitly controlled by the coupling constants and the principal curvatures of the surface. This effect is completely new compared to lower dimensional critical situations or special geometries considered up to now, in which only a single new point in the essential spectrum was observed.

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