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

Abstract

We present a formulation of the Hamiltonian variational method for quantum electrodynamics (QED) that enables the derivation of a relativistic few-fermion wave equation that can account, at least in principle, for interactions to any order of the coupling constant. We derive a relativistic two-fermion wave equation using this approach. The interaction kernel of the equation is shown to be the generalized invariant [Formula: see text] matrix including all orders of Feynman diagrams. The result is obtained rigorously from the underlying quantum field theory (QFT) for an arbitrary mass ratio of the two fermions. Our approach is based on three key points: a reformulation of QED, the variational method, and adiabatic hypothesis. As an application, we calculate the one-loop contribution of radiative corrections to the two-fermion binding energy for singlet states with arbitrary principal quantum number n, and [Formula: see text] = J = 0. Our calculations are carried out in the explicitly covariant Feynman gauge.PACS Nos.: 12.20.–m