By use of Moyal's representation and a perturbation theory developed by the author, we remove the interband matrix elements of the Dirac Hamiltonian in the presence of external fields. The result is exact in terms of velocity, but appears as a series in the field strengths and their derivatives, which is evaluated to second order in the fields and first order in their first derivatives.

• Received 23 July 1962

DOI:https://doi.org/10.1103/PhysRev.128.2454