Confinement in non-linear classical field-theory: a model of Dirac quarks

Abstract

We present a model in which a hadron is represented as a bound state of several nonlinear Dirac fields which we identify with the quarks. These fields interact by a fourth order coupling term. We define a particle as any finite energy solitary wave solution of the field equations and we show that the model admits only two kinds of particles: a) three quark (or three antiquark) states and b) n(quark-antiquark) states, n = 1, 2, 3. The Dirac fields are never free and, as they cannot show up as particles because there are no one field solitary waves, they are absolutely confined.