Quantum electrodynamics based on self-energy, without second quantization: The Lamb shift and long-range Casimir-Polder van der Waals forces near boundaries

Using a previously formulated theory of quantum electrodynamics (QED) based on self-energy, we give a general method for computing the Lamb shift and related Casimir-Polder energies for a quantum system in the vicinity of perfectly conducting boundaries. Our results are exact and easily extendable to a full covariant relativistic form. As a particular example we apply the method to an atom near an infinite conducting plane, and we recover the standard QED results (which are known only in the dipole approximation) in a simple and straightforward manner. This is accomplished in the context of the new theory which is not second quantized and contains no vacuum fluctuations.