An operatorially solved model of massless two-dimensional quantum chromodynamics

Abstract

An operator solution is constructed in (1,1) dimensions to the massless quantum chromodynamics of n fermion quarks and n 2 − 1 vector boson gluons with local colour SU( n) symmetry. The interacting quark field is a confined SU( n) Thirring field with zero Abelian coupling. The colour gluons are dependent Lie fields obeying the gluon-free fermionic current identity. Explicit local infinitesimal operator colour transformations (with an arbitrary coordinate-independent Lorentz vector coefficient defining the gauge) are given and the requirement of proper colour covariance linked to the vanishing of the coloured quark source currents and hence to the absence of coloured quark-composite states. The status of Noether's theorem is also clarified.