Dynamical symmetry breakdown in two-dimensional quantum chromodynamics. I. Massless quarks

Abstract

In this paper, the first of a trilogy on SU(N) quantum chromodynamics in 1+1 dimensions, the case of massless quarks is considered. Using an analog of the indefinite-metric formalism of Lowenstein and Swieca, we construct an explicit operator solution to this theory. This confirms Patrascioiu's conjecture that the SU(N) symmetry in this theory is broken down to S[U(1)]^N and that there are N−1 massive quarkantiquark bound states in addition to a massless one. This bound-state spectrum also agrees with some earlier work done in the N→∞ limit. The spontaneous nature of the dynamically induced symmetry breakdown is elaborated upon and the degeneracy of the vacuum is exhibited. We illuminate the essentially nonperturbative feature of this phenomenon.