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- W2963981850 abstract "We show how to construct, using an elementary extension of the Pinch Technique (PT), all offshell Green’s functions of a non-Abelian gauge theory so tha t 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. These PT-RGI Green’s functions are those of the gaug e potentials gAν , which is RGI itself in the PT. They differ from the standard PT Green’s functions by a simple multiplicative factor that removes their dependence on the renormalization point μ. Closed quark and ghost loops do not change this. We outline how to construct an approximate PT-RGI three-gluon vertex with three physical momentum scales but no μ-dependence, possibly phenomenologically useful. PTRGI Green’s functions obey a hierarchy of Schwinger-Dyson e quations (SDEs) that is organized by their momentum dependence in the UV, which can be found exactly from this hierarchy using the PT Ward identities. One of these Ward identities yields the gluon propagator as a functional of the vertex, allowing for an SDE truncation that is just the opposite of the often-used gauge technique that expresses the vertex approximately as a functional of the propagator, but which mishandles the UV behavior. Gluonic spin furnishes complications that would take too long to explain fully here, so we give details of this SDE hierarchy f or an analogous vertex and propagator in a modified form of φ 3 6 theory. The PT-RGI property of all off-shell Green’s functi ons, plus other long-known features of NAGTs coupled to quarks, leads to near-realization of the dreams of S-matrix theorists of the sixties: An effectively finite t heory whose symmetry structure (that of an NAGT) follows from unitarity, and having no fixed singul arities in angular momentum. Effective finiteness means that all Green’s functions, incl uding matrix elements of condensates, depend neither on a cutoff nor on a renormalization point μ; in conventional treatments, an offshell Green’s function will depend either on one (unrenorma lized, cutoff-dependent) or the other (renormalized, μ-dependent)." @default.
- W2963981850 created "2019-07-30" @default.
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- W2963981850 date "2012-02-20" @default.
- W2963981850 modified "2023-09-23" @default.
- W2963981850 title "Renormalization group invariance in the Pinch Technique" @default.
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- W2963981850 doi "https://doi.org/10.22323/1.136.0010" @default.
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