Abstract
A few years ago, based on standard functional manipulations, an unexpected property was proven to be satisfied by the fermionic Green's functions of QCD, and dubbed effective locality. This feature of QCD is non-perturbative as it results from a full integration of the fermionic and gluonic degrees of freedom. Previous derivations of effective locality are reviewed, corrected, and enlarged. Focussing on the way nonabelian gauge invariance is realized in the non-perturbative regime of QCD, the meaning of effective locality is proposed.
Highlights
In a series of recent articles [1,2,3,4,5] a property of the non-perturbative fermionic Green’s functions of QCD has been put forward under the name effective locality, and at face value this property can be summarized as follows.For any fermionic 2n-point Green’s functions and related amplitudes, the full gauge-fixed sum of linear, cubic and quartic gluonic interactions, fermionic loops included, results in a local contacttype interaction
In the pure euclidean Yang Mills case, though, and up to the first non-trivial orders of a semi-classical expansion, effective locality was observed a welcome property in an attempt to construct a formulation dual to the original Yang Mills theory [6]
Like in the pure Yang Mills situation of [6], effective locality offers a useful means to learn about nonperturbative physics in QCD, and this based on first principles and standard functional operations
Summary
In a series of recent articles [1,2,3,4,5] a property of the non-perturbative fermionic Green’s functions of QCD has been put forward under the name effective locality, and at face value this property can be summarized as follows. Like in the pure Yang Mills situation of [6], effective locality offers a useful means to learn about nonperturbative physics in QCD, and this based on first principles and standard functional operations To begin with, it is worth reviewing the constructions of the Green’s functions generating functionals of QED and QCD, and to contrast them at one essential point. The statement of effective locality can be exposed in the simpler situation where it was first discovered [1], before being extended to the full non approximated theory [2] In these two previous cases, made was used of socalled Schwinger/Fradkin’s representations for a quark propagating in a background gluonic field. Though, effective locality holds true irrespective of Schwinger/Fradkin’s representations, and this helps to disclose one of the deepest aspect of this newly discovered property [7]
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