QLunch: Distinguished self-adjoint extensions of operators with gaps
Speaker: Sabiha Tokus from QMATH
Title: Distinguished self-adjoint extensions of operators with gaps
Semibounded symmetric operators have a distinguished self-adjoint extension, the Friedrichs extension. The eigenvalues of the Friedrichs extension are given by the famous Rayleigh-Ritz variational principle. Dirac operators describing relativistic particles are not semibounded. Nevertheless the Dirac-Coulomb operator is known to have a distinguished extension. I relate it to a generalization of the Friedrichs extension to the setting of operators with gaps and give the corresponding variational principle.
This is joint work with Lukas Schimmer and Jan Philip Solovej.