From quantum electrodynamics to mean-field theory. II. Variational stability of the vacuum of quantum electrodynamics in the mean-field approximation

For pt.I see ibid., vol.22, no.23, p.3791-814 (1989). The authors use a minimisation principle to analyse the variational stability of the translationally invariant vacuum of quantum electrodynamics, with a Coulomb two-body interaction. They show how the magnitude of the coupling constant alpha determines the existence of a stable variational ground state. This ground state does exist within the considered variational space, provided that alpha is smaller than a critical value alpha _c. The ground state collapses if alpha is larger than alpha _c. Bounds on the critical value alpha _c are given, and the physical value alpha =1/137 is shown to be undercritical.