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Renormalization group invariance in the Pinch Technique

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 $μ$. Properties of the PT-RGI Schwinger-Dyson equations are discussed, mostly in the context of a modified form of $ϕ^3_6$. 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.