A New Approach to Analytic, Non-Perturbative and Gauge-Invariant QCD

TL;DR

This paper introduces a novel, non-perturbative, gauge-invariant analytic approach to QCD, revealing a new 'Effective Locality' property that simplifies the calculation of quark interactions and bound states.

Contribution

It presents a non-perturbative, gauge-invariant evaluation of the QCD generating functional using Fradkin representations, introducing 'Effective Locality' to simplify quark interaction calculations.

Findings

Derived quark-antiquark binding potential for pions.

Calculated three-quark binding potential for nucleons.

Demonstrated the simplification of functional integrals to ordinary integrals.

Abstract

Following a previous calculation of quark scattering in eikonal approximation, this paper presents a new, analytic and rigorous approach to the calculation of QCD phenomena. In this formulation a basic distinction between the conventional "idealistic" description of QCD and a more "realistic" description is brought into focus by a non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of the exact Fradkin representations of the Green's functional and the vacuum functional. Because quarks exist asymptotically only in bound states, their transverse coordinates can never be measured with arbitrary precision; the non-perturbative neglect of this statement leads to obstructions that are easily corrected by invoking in the basic Lagrangian a probability amplitude which describes such transverse imprecision. The second result of this non-perturbative analysis is the appearance of a new and simplifying output called "Effective Locality", in which the interactions between quarks by the exchange of a "gluon bundle" - which "bundle" contains an infinite number of gluons, including cubic and quartic gluon interactions - display an exact locality property that reduces the several functional integrals of the formulation down to a set of ordinary integrals. It should be emphasized that "non-perturbative" here refers to the effective summation of all gluons between a pair of quark lines, but does not (yet) include a summation over all closed-quark loops which are tied by gluon-bundle exchange to the rest of the "Bundle Diagram". As an example of the power of these methods we offer as a first analytic calculation the quark-antiquark binding potential of a pion, and the corresponding three-quark binding potential of a nucleon, obtained in a simple way from relevant eikonal scattering approximations.