Quantum electrodynamics with “two-particle” unitarity: Charged spin-0 bosons

The spin-0 propagator in quantum electrodynamics of charged spinless bosons (“pions”) is investigated in detail via the closest approximation to the Schwinger-Dyson equation in the two-particle unitarity approximation proposed initially by Salam by replacing the photon propagator by its zero order result. The high-energy behavior (in spacelike directions) of the (renormalized) spin-0 propagator Δ(p²) is explicitly derived and a finite electromagnetic mass excitation for the “pion” is obtained. The latter follows as a result of the derived asymptotic behavior of Δ^?1(p²) (p² → ∞) that the unrenormalized mass m₀ ≡ 0. This brings us into contact with earlier work of Johnson, Landau and their collaborators. The fact that m₀² ≡ 0 and that Δ^?1(p²)/_p²=?m² = 0 (m ≠ 0) (in Nambu's sense) gives us an eigenvalue equation for the fine structure constant which may be then computed in terms of no other parameters. This eigenvalue equation is expanded in powers of the coupling constant with all the expansion coefficients being finite. The latter is computed to sixth order in the charge.