Gauge-invariant resummation formalism for two-point correlation functions

The consistent description of unstable particles, renormalons, or other Schwinger-Dyson-type 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 the issues of the uniqueness of the resummation procedure related to the latter method.