Baryonlike and mesonlike solitons in a one-dimensional Dirac model of extended particles

Abstract

A version in 1+1 dimensions of a recently proposed model of an extended particle with confined constituents is presented. Several constitutive spinors, considered as classical c numbers, interact through a vector coupling. There are no solutions in which only one field is nonvanishing, because each of them acts as a source of the rest, so that they cannot be separated in any way. This gives a mechanism of confinement which operates at the classical level. Moreover, the bound states have the characteristic three-quark and quark-antiquark patterns and their analytic expression can be given in terms of the Thirring solitons. They keep their identity upon collisions, at least between particlelike solutions of the same kind. Accordingly, they are called baryonlike and mesonlike solitons.