DELTA-EXPANSION APPLIED TO QUANTUM ELECTRODYNAMICS

A recently proposed technique known as the delta-expansion provides a nonperturbative treatment of a quantum field theory. The 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 delta-expansion is equivalent to a fermion loop expansion. That is, the coefficient of delta(n) in the 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 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 delta-expansion we perform a speculative calculation of the fermion condensate in the massive Schwinger model in the limit of large coupling constant.