Derivation of Nonrelativistic Hamiltonian for Electrons from Quantum Electrodynamics

The effective quantum-mechanical Hamiltonian for a system of electrons in static electromagnetic field is derived from quantum electrodynamics for electron velocities small compared with the light velocity. The Hamiltonian obtained is almost identical with the one obtained by Bethe and Salpeter, but there is a small difference, of which an explanation is given.