Semiclassical random electrodynamics: spontaneous emission and the Lamb shift

Abstract

It is often remarked that an explanation of spontaneous emission and the Lamb shift requires quantization of the electromagnetic field. Here these two quantities are derived in a semiclassical formalism by use of second-order perturbation theory. The purpose of the present paper is not to argue the validity of QED but rather to develop a semiclassical approximation to QED that may nonetheless have certain computational advantages over QED. To this end, the vacuum of QED is simulated with a classical zero-point field (ZPF), and as a consequence the resulting theory is entitled semiclassical random electrodynamics (SRED). In the theory, the atom is coupled to the ZPF and to its own radiation-reaction field through an electric dipole interaction. These two interactions add to produce exponential decay of excited states while they cancel each other to prevent spontaneous excitation of the ground state; the Lamb shift appears in the theory as an ac Stark shift induced by the ZPF. The spontaneous decay rate of an excited-state derived in SRED is equal to the Einstein A coefficient for that state, and the Lamb shift agrees with that of nonrelativistic QED. Moreover, SRED is shown to be useful for the numerical simulation of spontaneous decay.