The quasi-abelian limit
1 Department of Physics,
Providence, RI 02912, USA
2 Institut Non Linéaire de Nice, 1361 Route des Lucioles, 06560 Valbonne, France
3 LPTHE, Tour 16, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France
Received: 30 August 1999 /Published online: 17 March 2000 - © Springer-Verlag 2000
A new, non perturbative, eikonal method called the ``quasi abelian limit'' (QAL) is suggested for high energy quark (nucleon) scattering involving the exchange of all possible, non interacting, non abelian gluons (mesons). With this method, those functional integrals defining, e.g., the exchange of color cooordinates in quark-quark scattering, are replaced by a finite number of quadratures over a subset of their coordinates. Mathematically, this procedure is not rigourous, because an unjustified interchange of limits has been performed; physically, it corresponds to the observation that the non perturbative sum over all color-moment fluctuations can vanish at arbitrarily high energies. The QAL generates a result in agreement with a corrected, ``contiguity'' calculation, when the latter is summed over all perturbative orders.
Copyright Società Italiana di Fisica, Springer-Verlag 2000