A Matrix Model for QCD: QCD Colour is Mixed

Abstract

We use general arguments to show that coloured QCD states when restricted to gauge invariant local observables are mixed. This result has important implications for confinement: a pure colourless state can never evolve into two coloured states by unitary evolution. Furthermore, the mean energy in such a mixed coloured state is infinite. Our arguments are confirmed in a matrix model for QCD that we have developed using the work of Narasimhan and Ramadas and Singer. This model, a $(0+1)$-dimensional quantum mechanical model for gluons free of divergences and capturing important topological aspects of QCD, is adapted to analytical and numerical work. It is also suitable to work on large $N$ QCD. As applications, we show that the gluon spectrum is gapped and also estimate some low-lying levels for $N=2$ and 3 (colors). Incidentally the considerations here are generic and apply to any non-abelian gauge theory.