Variational Two Fermion Wave Equations in QED

Abstract

We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-state variational trial function is used to derive relativistic two-fermion equations variationally from the expectation value of the Hamiltonian of the field theory. The interaction kernel of the equation is shown to be, in essence, the invariant M matrix in lowest order. Solutions of the two-body equations are presented for muonium like system for small coupling strengths. The results compare well with the observed muonium spectrum, as well as that for hydrogen and muonic hydrogen. Anomalous magnetic moment effects are discussed.

Interparticle potentials in a scalar quantum field theory with a Higgs-like mediating field

“…We shall use a reformulated Hamiltonian formalism, together with the variational method, to accomplish this task. This approach has been used effectively in the study of few-boson states in the scalar Yukawa theory [3,4] and relativistic few-fermion bound states in relativistic quantum mechanics [5] and QED [6,7].…”