Relativisticn-fermion wave equations in quantum electrodynamics

Abstract

The variational method in a reformulated Hamiltonian formalism of quantum electrodynamics is used to derive relativistic wave equations for a system consisting of $n$ fermions and antifermions. Simple Fock-space variational trial states are used to obtain the relativistic $n$-body equations. The derived kernels of these equations (i.e., momentum-space relativistic potentials) include one-photon exchange and virtual annihilation interactions. The equations are shown to have the Schr\odinger nonrelativistic limit. Application to the particular cases of positronium (Ps), positronium negative ion $({\text{Ps}}^{\ensuremath{-}})$, and positronium molecule (${\text{Ps}}_{2}$, ${e}^{\ensuremath{-}}{e}^{+}{e}^{\ensuremath{-}}{e}^{+}$) are discussed.