  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.
