Maria J. Esteban: Critical magnetic fields for the Dirac-Coulomb operator

In this talk I will present a study about the coupling of the Dirac operator with a Coulomb potential and a constant magnetic potential. This is a model for an electron submitted to the action of an external electromagnetic field. We show that there is a critical magnetic field beyond which the electron becomes unstable. We also compare the critical field for general electron wave-functions and for functions in the first Landau level. We prove that the two are very far from each other for small electrical fields.