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

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Summary

Introduction

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.

The 4–Point Fermionic Green’s Function
Effective Locality as General, Still Formal a Statement
Theoretical Aspects of Effective Locality
Fradkin’s Representation Independence
An Odd Term: δ(2) (~b)
Integration
Effective Locality and Meijer Special Functions
Colour Algebraic Structure of Fermionic Green’s Functions
EL Calculations
An Effective Perturbative Expansion for the Strong Coupling Regime
EL and Dynamical Chiral Symmetry Breaking
Quark–Quark Binding Potential
Estimation of the Light Quark Mass
Nucleon–Nucleon Binding Potential
Estimation of the Size of the Deuteron
Application to pp Elastic Scattering
Conclusions
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