Curvature Contribution to the Essential Spectrum of Dirac Operators with Critical Shell Interactions

Explore the characterization of the essential spectrum of three-dimensional Dirac operators with critical shell interactions in this 55-minute seminar from the Spectral Geometry in the clouds series. Delve into the rigorous definition and basic spectral properties of perturbed operators, focusing on critical combinations of electrostatic and Lorentz scalar shell interactions supported on smooth compact surfaces. Discover how the essential spectrum within the gap of the free Dirac operator is influenced by surface geometry, with the criticality of the interaction leading to a new interval explicitly controlled by coupling constants and principal curvatures. Learn about the unique case of a sphere, where this interval reduces to a single point. Gain insights from this collaborative work between Badreddine Benhellal and Konstantin Pankrashkin from Carl von Ossietzky Universität Oldenburg, presented at the Centre de recherches mathématiques - CRM.