In this paper, the first of a trilogy on $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ 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 $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ symmetry in this theory is broken down to $S{\left[\mathrm{U}\mathrm{}\right(1\left)\right]}^N$ and that there are $N-1\mathrm{}$ massive quarkantiquark bound states in addition to a massless one. This bound-state spectrum also agrees with some earlier work done in the $N\to \infty$ 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.

Close

PrevNext

View figure in article