Delta expansion applied to quantum electrodynamics.

Abstract

A recently proposed technique known as the \ensuremath{\delta} expansion provides a nonperturbative treatment of a quantum field theory. The \ensuremath{\delta}-expansion approach can be applied to electrodynamics in such a way that local gauge invariance is preserved. In this paper it is shown that for electrodynamic processes involving only external photon lines and no external electron lines the \ensuremath{\delta} expansion is equivalent to a fermion loop expansion. That is, the coefficient of ${\mathrm{\ensuremath{\delta}}}^{\mathit{n}}$ in the \ensuremath{\delta} expansion is precisely the sum of all n-electron-loop Feynman diagrams in a conventional weak-coupling approximation. This equivalence does not extend to processes having external electron lines. When external electron lines are present, the \ensuremath{\delta} expansion is truly nonperturbative and does not have a simple interpretation as a resummation of conventional Feynman diagrams. To illustrate the nonperturbative character of the \ensuremath{\delta} expansion we perform a speculative calculation of the fermion condensate in the massive Schwinger model in the limit of large coupling constant.