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

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.
Comment: 21 pages, 3 figures, the third piece of a series (Eur. Phys. J. C65, 395 (2010) and arXiv:1003.2936[hep-th]). Additional proof has been added along with 2 appendices for more details in the main text