An explicit form of a colour-singlet Fermion field is constructed from the operator solution ofSU(n) Thirring model where the quark-fields are known to be confined in LSZ sense. In simple cases of massless quarks these ferions are free with zero mass and can be expressed as the antisymmetric composites of constituent quark fields. This simple exercise suggests an altemative to conventional two-dimensional QCD which seems to confine all Fermion including baryons by Schwinger mechanism.
In recent years a large amount of research has been made on the nonperturbative aspects of QCD in a kinematicaUy simpler domain of space-time of (1 + 1) dimensions. The measure of success of all these models have been the explicit demonstration of colour confmement and explaining the meson-spectrum as the colour-singlet q~ composites. There has been a wide range of differences about the nature of the gtuons -whether they remain massless or acquire mass through some dynamical breakdown of symmetry and whether they are observable or not. However, very little progress has been made on the investigations of baryons as colour-singlet composites of odd number of quarks -an aspect without which the theory of strong interaction is never complete. The basic reasons for such lack are (i) the difficulties of handling three or higher-body problems by Bethe-Salpeter methods in 't Hooft-like models [1 ] and (ii) the screening of all Fermions due to dynamical generation of masses of the gauge fields in Schwinger-like models.
The purpose of this paper is to explore the existence of multiquark colour-singlet Fermionic composite fields in a model of QCD2 suggested by Probir Roy and this author [2]. Strictly speaking, in spite of its resemblance with the conventional QCD, it is a more trivial theory with no gluonic degrees of freedom. Though the quark masses have been taken to be zero, inclusion of soft mass will not change the basic construction. However, such mass will make the baryonic solitons interacting. We will avoid such complication and be content with the fact that even in the massless situation one can see all the desirable observable features of strong interaction, namely the confinement of all the coloured states (with quarks in particular) and the existence of colour singlet mesonic and baryonic states.
Any Schwinger-like model will topologically confme the baryonic states. This is beacuse the conserved observable current Ju -euv Ovq~ will have a consistent field-current algebra only when F(q~) = l-qq~ will satisfy a certain periodicity condition [3]. But such a condition is violated when ~b has a dynamically generated mass as in a Schwinger model. In order that the Fermions be observable either q~ should be massless or it has to satisfy a Sine-Gordon equation of motion.