English

Renormalization group invariance in the Pinch Technique

High Energy Physics - Theory 2011-11-03 v1 High Energy Physics - Phenomenology

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 μ\mu. Properties of the PT-RGI Schwinger-Dyson equations are discussed, mostly in the context of a modified form of ϕ63\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.

Keywords

Cite

@article{arxiv.1111.0322,
  title  = {Renormalization group invariance in the Pinch Technique},
  author = {John M. Cornwall},
  journal= {arXiv preprint arXiv:1111.0322},
  year   = {2011}
}

Comments

12 pages, 2 figures; invited talk at the International Workshop on QCD Greens Functions, Confinement, and Phenomenology, September 2011

R2 v1 2026-06-21T19:29:20.320Z