Bound State Corrections in Two-Body Systems

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Abstract
Available expressions for two-body equations contain an interaction kernel which treats particles in intermediate states as free. In situations where the binding is important, such as the calculation of low-energy electrodynamic corrections, a more accurate treatment is necessary. A satisfactory formalism is developed for systems in which an instantaneous interaction is responsible for the binding. The procedure may then be used to evaluate the effects of small retarded perturbations. It consists of summing those binding interactions which occur during the retarded perturbations and which never should have been expanded as "small" effects. The result is expressed in terms of the two-body Green's function of the instantaneously interacting system. This function occurs to describe the propagation of the two particles in the intermediate state. The relative time coordinate does not appear explicitly in the formulas. The method is applied to the calculation of the hyperfine structure of positronium. The infrared divergences which occurred in a previous investigation of this effect are eliminated by the new approach.

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