The Exact Electron Propagator in a Magnetic Field as the Sum over Landau   Levels on a Basis of the Dirac Equation Exact Solutions
  The exact propagator for an electron in a constant uniform magnetic field as the sum over Landau levels is obtained by the direct derivation by standard methods of quantum field theory from exact solutions of the Dirac equation in the magnetic field. The result can be useful for further development of the calculation technique of quantum processes in an external active medium, particularly in the conditions of moderately large field strengths when it is insufficient to take into account only the ground Landau level contribution. 
A.V. Kuznetsov and A. A. Okrugin (Yaroslavl State (P.G. Demidov)   University, Russia)
hep-ph hep-th