Renormalization group invariance in the Pinch Technique

TL;DR

This paper introduces a method to construct gauge-invariant, renormalization-group invariant off-shell Green's functions in non-Abelian gauge theories, enhancing their physical interpretability and process independence.

Contribution

It extends the Pinch Technique to produce PT-RGI Green's functions that are gauge-invariant, process-independent, and satisfy Ward identities, with an application to the three-gluon vertex.

Findings

Construction of PT-RGI Green's functions with physical scales

Development of an approximate three-gluon PT-RGI vertex

Discussion of PT-RGI Schwinger-Dyson equations in a modified ^3_6 context

Abstract

We show how to construct, using an elementary extension of the Pinch Technique, all off-shell Green's functions of a non-Abelian gauge theory so that they are locally gauge-invariant and renormalization-group invariant (RGI), as the S-matrix is, as well as being process-independent, coupling-constant independent (dimensional transmutation), and satisfying QED-like Ward identities. We call these PT-RGI Green's functions and outline how to construct an approximate three-gluon PT-RGI vertex with three physical scales and no dependence on the renormalization point $\mu$. Properties of the PT-RGI Schwinger-Dyson equations are discussed, mostly in the context of a modified form of $\phi^3_6$. The PT-RGI property of all off-shell Green's functions, plus other work of long ago, leads to a near-realization of the old dreams of S-matrix theorists.