Variational two-fermion wave equations in quantum electrodynamics: Muoniumlike systems

Abstract

We consider a reformulation of quantum electrodynamics 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 muoniumlike systems 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.

A short review about some exotic systems containing electrons, muons, and tauons

“…The resulting modified Hamiltonian contains the photon propagator directly. The authors [22] obtained solutions of the two-body equations for muoniumlike system to the order of Oða 4 Þ. Their results compare well with the observed muonium spectrum, as well as that for hydrogen and muonic hydrogen.…”

“…Their results compare well with the observed muonium spectrum, as well as that for hydrogen and muonic hydrogen. Anomalous magnetic moment effects are also discussed in [22].…”

“…Since then, this system (and muonium-like systems) have been investigated in the literature by many authors, particularly for the nonrelativistic case. For the relativistic and QED corrections of the muonium-like systems, there are some papers available in the literature (see, for example, [22] and refs therein).…”

“…Terekidi and Darewych [22] have considered 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.…”

“…The simplest system for fermions and antifermions of different flavor is muonium, e À l þ : This system (and muonium-like systems) have been investigated in the literature (see, for example, [22] and refs therein). The term ''muonium'' for the e À l þ bound state and its first theoretical discussion appeared in Ref.…”