  The Darwin-Breit Hamiltonian is applied to the Aharonov-Bohm experiment. In
agreement with the standard Maxwell-Lorentz theory, the force acting on
electrons from infinite solenoids or ferromagnetic rods vanishes. However, the
interaction energies and phase factors of the electron wave packets are
non-zero. This allows us to explain the Aharonov-Bohm effect without
involvement of electromagnetic potentials, fields, and topological properties
of space.
