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We present a formulation of the Hamiltonian variational method for QED whichenables the derivation of relativistic few-fermion wave equation that canaccount, at least in principle, for interactions to any order of the couplingconstant. We derive a relativistic two-fermion wave equation using thisapproach. The interaction kernel of the equation is shown to be the generalizedinvariant M-matrix including all orders of Feynman diagrams. The result isobtained rigorously from the underlying QFT for arbitrary mass ratio of the twofermions. Our approach is based on three key points: a reformulation of QED,the variational method, and adiabatic hypothesis. As an application wecalculate the one-loop contribution of radiative corrections to the two-fermionbinding energy for singlet states with arbitrary principal quantum number $n$,and $l =J=0$. Our calculations are carried out in the explicitly covariantFeynman gauge.Comment: 26 page

Bound-state variational wave equation for fermion systems in quantum electrodynamics