Field Renormalization and Reduction Formula in Quantum Electrodynamics

Abstract

An Ansatz is proposed for the asymptotic field of a charged particle which gives the known power-law behavior ${(p^2-m^2+i\epsilon )}^{-1-\beta }$, $\beta \ne 0$, for the electron propagator near the mass shell. This allows the electron-wave-function renormalization to be related to the normalization of the asymptotic field. A reduction formula is presented, expressing the $S$ matrix in terms of Green's functions which are evaluated according to a precise on-mass-shell renormalization prescription.