Eur. Phys. J. A 10, 309-346

Relativistic quark models of baryons with instantaneous forces

Theoretical background

U. Löring, K. Kretzschmar, B.Ch. Metsch and H.R. Petry

Institut für Theoretische Kernphysik, Universität Bonn, Nußallee 14-16, D-53115 Bonn, Germany

(Received: 27 March 2001 Communicated by V.V. Anisovich)

Abstract
This is the first of a series of three papers treating light baryon resonances (up to 3 GeV) within a relativistically covariant quark model based on the three-fermion Bethe-Salpeter equation with instantaneous two- and three-body forces. In this paper we give a unified description of the theoretical background and demonstrate how to solve the Bethe-Salpeter equation by a reduction to the Salpeter equation. The specific new features of our covariant Salpeter model with respect to the usual nonrelativistic quark model are discussed in detail. The purely theoretical results obtained in this paper will be applied numerically to explicit quark models for light baryons in two subsequent papers.

PACS
11.10.St - Bound and unstable states; Bethe-Salpeter equations.
12.39.Ki - Relativistic quark model.
12.40.Yx - Hadron mass models and calculations.
14.20.-c - Baryons (including antiparticles).

© Società Italiana di Fisica, Springer-Verlag 2001