Renormalization group invariance in the Pinch Technique

Details Renormalization group invariance in the Pinch Technique Renormalization group invariance in the Pinch Technique

2011-11-01

arxiv.org/abs/1111.0322v1

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, 2 figures; invited talk at the International Workshop on QCD Greens Functions, Confinement, and Phenomenology, Septe

Scientific paper

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.

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