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Abstract
Using the theory of quantum electrodynamics (QED) based on self-fields, as developed by Barut and his co-workers, we formulate a method to compute the effect of nontrivial boundary conditions on QED-type radiative corrections. Our approach is novel in that the radiation field is not second quantized and there are no zeropoint field fluctuations; all corrections arise in a simple fashion when the self-field of a charged particle is made to satisfy the appropriate boundary conditions.
We make explicit calculations and predictions in the following cases: Inhibition and enhancement of the spontaneous emission rate for a hydrogen atom near a single conducting plane, between two parallel planes and within a conducting sphere; the change of the Lamb shift and the associated Casimir-Polder van der Waals force for a hydrogen atom near a single conducting plane; and the change of the magnetic moment, mass and orbital frequency of an electron executing cyclotron motion near a single conducting wall. Our spontaneous emission and Lamb shift results compare well with existing experiments, and our magnetic moment calculation satisfactorily resolves a controversy in the recent literature over whether there exist boundary induced corrections of the spin precession frequency to order $\alpha$, where $\alpha$ is the fine structure constant. We give an overview of the self-field approach to QED versus the standard, second quantized approach. Finally we indicate how, by generalizing the concept of boundary, one may use the self-field approach to compute such phenomena as: the Hawking and Unruh effects, whereby an event horizon gives rise to a perceived, uniform bath of thermal radiation; and further results involving Casimir-Polder van der Waals forces.
