Relativisticn-fermion wave equations in quantum electrodynamics

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 (Ps^-), and positronium molecule (Ps₂, e^-e⁺e^-e⁺) are discussed.