H. M. Fried

Gauge-invariant summation of All QCD virtual gluon exchanges

The interpretation of virtual gluons as ghosts in the non-linear gluonic structure of QCD permits the formulation and realization of a manifestly gauge-invariant and Lorentz covariant theory of interacting quarks/anti-quarks, for all values of coupling. The simplest example of quark/anti-quark scattering in a high-energy, quenched, eikonal model at large coupling is shown to be expressible as a set of finite, local integrals which may be evaluated numerically; and before evaluation, it is clear that the result will be dependent only on, and is damped by increasing momentum transfer, while displaying a physically-reasonable color dependence in a manner underlying the MIT Bag Model and an effective, asymptotic freedom. Similar but more complicated integrals will result from all possible gluonic-radiative corrections to this simplest eikonal model. Our results are compatible with an earlier, field-strength analysis of Reinhardt et al.

Nontrivial generalizations of the Schwinger pair production result. II

It is suggested that Schwingers (1951) vacuum persistence probability against pair production by an intense but constant electric field is a very good approximation to the corresponding quantity if the field does not vary appreciably over space-time distances less than m{sup -1}(m{sup 2}/eE). This general result appears to be in agreement with a variety of previous calculations, both numerical and analytical.

A new approach to analytic, non-perturbative and gauge-invariant QCD

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 Green’s functional G c ( x , y | A ) and the vacuum functional L [ A ] . 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–which may be the same quark line, as in a self-energy graph–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. A second calculation, analytic, non-perturbative and gauge-invariant, of a nucleon–nucleon binding potential to form a model deuteron, will appear separately.

Analytic, non-perturbative, gauge-invariant quantum chromodynamics: Nucleon scattering and binding potentials

Abstract 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 the transverse imprecision of quark coordinates, is again used, while the strength of the potential is proportional to the square of a renormalized quantum chromodynamics (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.

Non-perturbative QCD amplitudes in quenched and eikonal approximations

Abstract Even though approximated, strong coupling non-perturbative QCD amplitudes remain very difficult to obtain. In this article, in eikonal and quenched approximations at least, physical insights are presented that rely on the newly-discovered property of effective locality . The present article also provides a more rigorous mathematical basis for the crude approximations used in the previous derivation of the binding potential of quarks and nucleons. Furthermore, the techniques of Random Matrix calculus along with Meijer G-functions are applied to analyze the generic structure of fermionic amplitudes in QCD.

Non-Abelian eikonals

A functional formulation and partial solution is given of the non-Abelian eikonal problem associated with the exchange of noninteracting, charged or colored bosons between a pair of fermions, in the large {ital s} small {ital t} limit. A simple, functional {open_quotes}contiguity{close_quotes} 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 nontrivial order agrees with the corresponding SU({ital N}) perturbative amplitude, while higher-order contributions to this eikonal generate an {open_quotes}effective Reggeization{close_quotes} 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({ital N}). {copyright} {ital 1997} {ital The American Physical Society}

On the summation of Feynman graphs

Abstract 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 increasing 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 Z 3 .

QED vacuum loops and vacuum energy

A QED-based “bootstrap” mechanism is suggested as a possible source of vacuum energy. In place of the conventional assumption that the vacuum expectation value of the current operator jμ vanishes in the absence of a classical, external field, one notes the possibility that, on very small scales, the vacuum fluctuations can generate an equation for an effective, C-number

Summing all the eikonal graphs. II

{A}_{\mu}^{\mathrm{ vac}}

On the non-perturbative realization of QCD gauge-invariance

giving rise to a finite and computable vacuum energy.