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

作者：Fried H M; Grandou T; Sheu Y M^*

来源：Annals of Physics, 2012, 327(11): 2666-2690.

DOI：10.1016/j.aop.2012.07.008

• Gauge invariance
• Non-perturbative QCD
• Functional technique
• Effective locality
• Bundle diagram
• Quark binding potential

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 %26quot;idealistic%26quot; description of QCD and a more %26quot;realistic%26quot; 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%26apos;s functional G(c)(x, y vertical bar 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. %26lt;br%26gt;The second result of this non-perturbative analysis is the appearance of a new and simplifying output called %26quot;Effective Locality%26quot;, in which the interactions between quarks by the exchange of a %26quot;gluon bundle%26quot; - which %26quot;bundle%26quot; 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 %26quot;non-perturbative%26quot; 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 %26quot;Bundle Diagram%26quot;. 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.

• 出版日期2012-11