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

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.Comment: 38 pages, 3 figures in REVTeX. Collections of follow-on work of Eur. Phys. J. C65, pp. 395-411 (2010). arXiv admin note: text overlap with arXiv:1103.4179, arXiv:1104.4663, arXiv:1003.293

Non-abelian Eikonals

A functional formulation and partial solution is given of the non-abelian eikonal problem associated with the exchange of non-interacting, charged or colored bosons between a pair of fermions, in the large $s$/small $t$ limit. A simple, functional ``contiguity" prescription is devised for extracting those terms which exponentiate, and appear to generate the leading, high-energy behavior of each perturbative order of this simplest non-abelian eikonal function; the lowest non-trivial order agrees with the corresponding SU(N) perturbative amplitude, while higher-order contributions to this eikonal generate an ``effective Reggeization" of the exchanged bosons, resembling previous results for the perturbative amplitude. One exact and several approximate examples are given, including an application to self-energy radiative corrections. In particular, for this class of graphs and to all orders in the coupling, we calculate the leading-log eikonal for SU(2). Based on this result, we conjecture the form of the eikonal scattering amplitude for SU(N).Comment: 19 pages, late

Non-perturbative QCD amplitudes in quenched and eikonal approximations

Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations, physical insights are presented that rely on the newly-discovered property of Effective Locality.Comment: Revised version (28 pages and 1 figure in REVTeX). Follow-up work of Eur. Phys. J. C65, pp. 395-411 (2010), (arXiv:1204.2038 [hep-ph]), and Ann. Phys. 327, pp. 2666-2690 (2012), (arXiv:1203.6137 [hep-ph]

Analytic, Non-Perturbative, Gauge-invariant QCD: Nucleon Scattering and Binding Potentials

Removal of the quenched approximation in the mechanism which produced an analytic estimate of quark-binding potentials, along with a reasonable conjecture of the color structure of the nucleon formed by such a binding potential, is shown to generate an effective, nucleon scattering and binding potential. The mass-scale factor on the order of the pion mass, previously introduced to define transverse imprecision of quark coordinates, is again used, while the strength of the potential is proportional to the square of a renormalized QCD coupling constant. The potential so derived does not include corrections due to spin, angular momentum, nucleon structure, and electroweak interactions; rather, it is qualitative in nature, showing how Nuclear Physics can arise from fundamental QCD.Comment: 25 pages, 3 figures in REVTeX. The fifth of a series on Non-Perturbative QCD (Eur. Phys. J. C65, 395 (2010) or arXiv:0903.2644 [hep-th], arXiv:1003.2936 [hep-th], arXiv:1103.4179 [hep-th] and arXiv:1104.4663 [hep-th].

Possibilities of a QED-Based Vacuum Energy

A QED-based bootstrap mechanism, appearing at sufficiently small space-time scales, is suggested as an explanation for the "dark" vacuum energy that may be able to accelerate the universe. Very small-scale vacuum currents are allowed to generate small-scale electromagnetic fields, which become significant near the light cone. The resulting lepton-pair production, some of which may be tachyonic, has ramifications for the convergence of all QED perturbative processes, as well as providing possible mechanisms for "dark" matter, galactic gamma-ray bursts, and ultra-high-energy cosmic rays.Comment: 20 pages, 1 tabl