English

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

Mathematical Physics 2009-11-13 v2 math.MP Spectral Theory

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.

Keywords

Cite

@article{arxiv.0709.1034,
  title  = {Heat kernel estimates and spectral properties of a pseudorelativistic operator with magnetic field},
  author = {D. H. Jakubassa-Amundsen},
  journal= {arXiv preprint arXiv:0709.1034},
  year   = {2009}
}