Heat kernel estimates and spectral properties of a pseudorelativistic operator with magnetic field

Abstract

Based on the Mehler heat kernel of the Schroedinger operator for a free electron in a constant magnetic field an estimate for the kernel of E_A is derived, where E_A represents the kinetic energy of a Dirac electron within the pseudorelativistic no-pair Brown-Ravenhall model. This estimate is used to provide the bottom of the essential spectrum for the two-particle Brown-Ravenhall operator, describing the motion of the electrons in a central Coulomb field and a constant magnetic field, if the central charge is restricted to Z below or equal 86.