A new, analytic, non-perturbative, gauge-invariant formulation of realistic QCD

This Formulation [1], [2], [3] is New, in the sense that it is less than 3 years old. But it could have been done decades ago, since the input information existed, but was overlooked. It is Analytic in the sense that physically-reasonable approximations can be estimated with paper and pencil; and exact amplitudes can be calculated as Meijer G-functions of various orders. It is Non-Perturbative in the sense that sums over all possible gluon exchanges between any pair of quarks and/or antiquarks, including cubic and quartic gluon interactions, are exactly performed. These multiple gluon exchanges combine into "Gluon Bundles" (GBs), as sums over Feynman graphs with finite numbers of exchanged gluons are replaced by "Bundle Graphs". In effect, gluons disappear from the formalism, and GBs remain as the effective carrier of all interactions between quark lines. A simple re-arrangement of the Schwinger/Symanzik functional solution for the Generating Functional of QCD - a rearrangement possible in QCD but not in QED - produces a formal statement of Gauge-Invariance, even though the formulation contains gauge-dependent gluon propagators. After the non-perturbative sums produce GBs, one sees explicit cancelation of all gauge-dependent gluon propagators; gauge-invariance is achieved as gauge-independence. A new insight into Realistic QCD appears in the non-perturbative domain, because quarks do not have individual asymptotic states; they are always asymptotically bound, and their transverse coordinates cannot, in principle, be measured exactly. "Transverse Imprecision" is introduced into the basic Lagrangian, and quark-binding potentials for the construction of mesons and nucleons can then be defined and evaluated. And the greatest surprise of all: A new, non-perturbative property appears, called Effective Locality, with the result that all functional integrals reduce to (a few) sets of ordinary integrals, easy to estimate approximately, or calculate on a desk-top computer. A fantastic simplification! With the aid of the above techniques, this presentation will describe each of the above paragraphs, with explicit descriptions of gauge-invariance, of the summation of all relevant Feynman graphs, of quark-binding into hadrons, and of nucleon-nucleon binding to form a deuteron. To our knowledge, the latter calculation is the first analytic example of Nuclear Physics obtained directly from basic QCD.