Some Remarks About Virtual Annihilation Interactions in Relativistic n-Body Wave Equations in QED

The existence of entities consisting of electrons and positrons was predicted in 1946 by J. A. Wheeler and he called them polyelectrons. The simplest bound-state is called positronium (Ps, e − e + ). Wheeler speculated that two Ps atoms may combine to form the di-positronium molecule (Ps 2 , e − e + e − e + ) which was finally observed in 2007. He also conjectured the existence of larger systems such as (Ps 3 , e − e + e − e + e − e + ). In a previous work the author has formulated the relativistic wave equations in quantum electrodynamics (QED) for a system consisting of n fermions and antifermions of equal masses where n can be any natural number and the equations contain relativistic effects up to the order of O ( α 4 ), α is the coupling. The kernels of the n -body wave equations in QED include one-photon exchange and virtual annihilation interactions. The latter interactions occur among pairs of fermions and antifermions. The equations have the Schrödinger non relativistic limit. In this manuscript, some points have been provided with respect to the virtual annihilation interactions for the few-body systems in addition to the particular cases of five- ( e − e + e − e + e − ) and six-body ( e − e + e − e + e − e + ) QED systems.