Quantum electrodynamics based on self-fields, without second quantization: Apparatus dependent contributions tog-2

Using a formulation of quantum electrodynamics which is not second quantized, but rather based on self-fields, we calculate the energy shifts of an electron bound by a magnetic field in the vicinity of an infinite-plane conductor. We confirm the recent result of Kreuzer that the energy shift arising from the plate-induced change in the magnetic moment, {Δ}{μ}/{μ}=-{α}/4Rm, is exactly canceled by a similar change {Δ}m/m=-{α}/4Rm in the mass. Thus no change occurs in the spin-precession frequency to order {α}/Rm, in agreement with Brown et al. This cancellation of the two effects resolves an apparent controversy in recent literature over whether such a shift to the spin-precession frequency ωₛ occurs. There is, however, a boundary-induced change in the cyclotron frequency ωc which we calculate in the quantum result as {Δ}ωc/ωc={α}/8Rm to order {α}. Our method of approach is novel in that it uses only the self-field to compute radiative corrections; there are no vacuum fluctuations.