A Non-Perturbative Gauge-Invariant QCD: Ideal vs. Realistic QCD

TL;DR

This paper distinguishes between idealized and realistic formulations of QCD, proposing a non-perturbative, gauge-invariant approach that incorporates limitations on quark position and momentum measurements, leading to more physically consistent predictions of hadron formation.

Contribution

It introduces a phenomenological modification to the QCD Lagrangian that accounts for measurement limitations, resolving inconsistencies in amplitude calculations and enabling realistic modeling of hadron and nucleon interactions.

Findings

Resolution of absurdities in QCD amplitude estimates

Introduction of effective quark binding potentials

Framework for realistic hadron formation

Abstract

A basic distinction, long overlooked, between the conventional, "idealistic" formulation of QCD, and a more "realistic" formulation is brought into focus by a rigorous, non-perturbative, gauge-invariant evaluation of the Schwinger solution for the QCD generating functional in terms of exact Fradkin representations for the Green's functional $\mathbf{G}_{c}(x,y|A)$ and the vacuum functional $\mathbf{L}[A]$. The quanta of all (Abelian) quantized fields may be expected to obey standard quantum-mechanical measurement properties, perfect position dependence at the cost of unknown momenta, and vice-versa, but this is impossible for quarks since they always appear asymptotically in bound states, and their transverse position or momenta can never, in principle, be exactly measured. Violation of this principle produces an absurdity in the exact evaluation of each and every QCD amplitude. We here suggest a phenomenological change in the basic QCD Lagrangian, such that a limitation of transverse precision is automatically contained in the now "realistic" theory, with the function essential to quark binding into hadrons appearing in the new Lagrangian. All absurdities in estimates of all "realistic" QCD amplitudes are then removed, and one obtains the possibility of hadron formation by appropriate quark binding potentials, and nucleon scattering and binding by effective, Yukawa-type potentials; the first of these potentials are constructed, in detail, in the following paper.