Approximation of Dirac Operators with Delta-Shell Potentials

Explore a 21-minute conference talk on the approximation of two-dimensional Dirac operators with electrostatic and Lorentz scalar δ-shell potentials supported on a straight line. Delve into the study of these singular potentials as idealized replacements for strongly localized potentials near a straight line. Examine the proof of convergence in norm resolvent sense, contrasting with existing literature's strong sense convergence. Investigate the conditions for interaction strengths, including the non-linear dependence on squeezed potential parameters. Learn about the unitary transformation approach for cases outside the standard parameter range. Gain insights from this presentation, which was part of the "Spectral Theory of Differential Operators in Quantum Theory" workshop at the Erwin Schrödinger International Institute for Mathematics and Physics, based on collaborative work with Jussi Behrndt and Markus Holzmann.