Geometrically Induced Discrete Eigenvalues of Dirac Operators with Lorentz Scalar Delta-Shell Interactions

Explore a 29-minute conference talk from the Workshop on "Spectral Theory of Differential Operators in Quantum Theory" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) in November 2022. Delve into the spectral properties of a two-dimensional Dirac operator with a real-valued constant Lorentz scalar δ-shell interaction supported on a broken line. Learn about the recent establishment of self-adjointness for this operator and discover how the essential spectrum compares to that of a Dirac operator with a δ-interaction on a straight line. Uncover the groundbreaking finding that for sufficiently small angles of the broken line, the discrete spectrum is always non-empty, marking the first demonstration of geometrically induced discrete eigenvalues in Dirac operators with singular potentials. Gain insights from this collaborative work involving D. Frymark and V. Lotoreichik, presented by Markus Holzmann.