Abstract
About ten years ago, the use of standard functional manipulations was demonstrated to imply an unexpected property 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 gauge invariant integration of the gluonic degrees of freedom. In this review article, a few salient theoretical aspects and phenomenological applications of this property are summarized.
Highlights
Apart from a supersymmetric extension [8], QCD is not known to admit any dual formulation and Effective Locality calculations themselves attest to this situation. It remains that Effective Locality calculations proceed from first principles and offer a useful means to learn about non-perturbative physics in QCD
The reason why EL calculations escape this dead end is that in the EL context, quantisation is achieved by functional differentiations, with the help of (9), rather than functional integrations with gauge-fixing terms
Quantization is carried out by relying on functional differentiations rather than functional integrations, the two procedures of quantization being equivalent whenever the Wick theorem applies to time-ordered products of quantum field operators
Summary
Over the past decade a number of articles has been devoted to the study of a new property concerning the non-perturbative regime of QCD [1–5]. For any fermionic 2n-point Green’s functions, the full gauge-fixed sum of cubic and quartic gluonic interactions, fermionic loops included, results in a local contact–type interaction. Apart from a supersymmetric extension [8], QCD is not known to admit any dual formulation and Effective Locality calculations themselves attest to this situation. It remains that Effective Locality calculations proceed from first principles and offer a useful means to learn about non-perturbative physics in QCD.
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