Gauge-Invariant Resummation Formalism for Two-Point Correlation Functions

Abstract

The consistent description of unstable particles, renormalons, or other Schwinger--Dyson-type of solutions within the framework of perturbative gauge field theories necessitates the definition and resummation of off-shell Green's functions, which must respect several crucial physical requirements. A formalism is presented for resummation of off-shell two-point correlation functions, which is mainly based on arguments of analyticity, unitarity, gauge invariance and renormalizability. The analytic results obtained with various methods, including the background field gauges and the pinch technique are confronted with the physical requirements imposed; to one-loop order the pinch technique approach satisfies all of them. Using renormalization group arguments, we discuss issues of uniqueness of the resummation procedure related to the latter method.