Propagator picture of the spatial confinement of quantized light emitted from an atom

A field-quantized electromagnetic propagator description emphasizing the spatial localization of light emitted from a single-electron atom is presented. With the aim of obtaining a better insight into the quantum electrodynamics in the near-field zone of the atom, two approaches, formally different but equivalent in respect to their physical predictions, are studied. From the Maxwell equations, among the transverse operators, a transverse propagator picture in which the source region for the field is identified with the spatial domain occupied by the transverse current density of the atom emerges. In this picture the field propagation is isotropic and always retarded. By identifying the source region with that of the total atomic current, the transverse propagator becomes anisotropic, and attains a nonretarded self-field part and a near-field part different from zero only for spacelike events. By changing the Coulomb Lagrangian, a nonrelativistic Hamiltonian formalism adequate for reconciling the photon concept with the anisotropic propagator picture is introduced. In this formalism the transverse self-field energy is transferred to the particle Hamiltonian, and the interaction Hamiltonian now includes an interaction between the retarded field and the transverse self-field dynamics. The link between the standard (nonpropagator) theory, often used to argue that the total electromagnetic field is always retarded, and the transverse propagator theory is established. The equivalence between the two approaches is proved by demonstrating that the standard theory in fact includes a nonretarded response in the spatial domain occupied by the longitudinal part of the induced atomic current density.