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

Abstract

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, \ensuremath{\Delta}\ensuremath{\mu}/\ensuremath{\mu}=-\ensuremath{\alpha}/4Rm, is exactly canceled by a similar change \ensuremath{\Delta}m/m=-\ensuremath{\alpha}/4Rm in the mass. Thus no change occurs in the spin-precession frequency to order \ensuremath{\alpha}/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 ${\ensuremath{\omega}}_{s}$ occurs. There is, however, a boundary-induced change in the cyclotron frequency ${\ensuremath{\omega}}_{c}$ which we calculate in the quantum result as \ensuremath{\Delta}${\ensuremath{\omega}}_{c}$/${\ensuremath{\omega}}_{c}$=\ensuremath{\alpha}/8Rm to order \ensuremath{\alpha}. Our method of approach is novel in that it uses only the self-field to compute radiative corrections; there are no vacuum fluctuations.