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].

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

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

QED vacuum loops and Inflation

A QED-based model of a new version of Vacuum Energy has recently been suggested, which leads to a simple, finite, one parameter representation of Dark Energy. An elementary, obvious, but perhaps radical generalization is then able to describe both Dark Energy and Inflation in the same framework of Vacuum Energy. One further, obvious generalization then leads to a relation between Inflation and the Big Bang, to the automatic inclusion of Dark Matter, and to a possible understanding of the birth (and death) of a Universe.Comment: 10 pages and 1 figure There has been a minor modification in the previous version (arXiv:1403.2651v1, 03/12/2014) : a reference has been added in [3] and an Appendix has been adde

The Birth and Death of a Universe

This letter is meant to be a brief survey of several recent publications providing a simple, sequential explanation of Dark Energy, Inflation and Dark Matter, which leads to a simple picture of the why and the how of the Big Bang, and thence to a possible understanding of the birth and death of a Universe.Comment: 4 pages, 1 figur

Non trivial generalizations of the Schwinger pair production result

We present new, non trivial generalizations of the recent Tomaras, Tsamis and Woodard extension of the original Schwinger formula for charged pair production in a constant field.Comment: 11 page

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]

On the Summation of Feynman Graphs

A functional method to achieve the summation of all Feynman graphs relevant to a particular Field Theory process is suggested, and applied to QED, demonstrating manifestly gauge invariant calculations of the dressed photon propagator in approximations of increas- ing complexity. These lead in a natural way to the extraction of the leading logarithmic divergences of every perturbative order, and to a demonstration of the possible cancellation of all such divergences in the calculation of the (inverse of the) photon's wavefunction renormalization constant Z3. This analysis provides a qualitative understanding of why the measured value of the renormalized fine structure constant is, approximately, 1/137