Quantum electrodynamics based on self-fields, without second quantization: Apparatus dependent contributions to g-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, Δμ/μ=-α/4Rm, is exactly canceled by a similar change Δm/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 ${\omega }_s$ occurs. There is, however, a boundary-induced change in the cyclotron frequency ${\omega }_c$ which we calculate in the quantum result as Δ${\omega }_c$/${\omega }_c$=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.