A Matrix Model for QCD: QCD Colour is Mixed

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.Comment: 16 pages, 3 figures. V2: comments regarding infinite energy and confinement adde

Spontaneous Breaking of Lorentz Symmetry and Vertex Operators for Vortices

We first review the spontaneous Lorentz symmetry breaking in the presence of massless gauge fields and infraparticles. This result was obtained long time ago in the context of rigorious quantum field theory by Frohlich et. al. and reformulated by Balachandran and Vaidya using the notion of superselection sectors and direction-dependent test functions at spatial infinity for the non-local observables. Inspired by these developments and under the assumption that the spectrum of the electric charge is quantized, (in units of a fundamental charge e) we construct a family of vertex operators which create winding number k, electrically charged Abelian vortices from the vacuum (zero winding number sector) and/or shift the winding number by k units. In particular, we find that for rotating vortices the vertex operator at level k shifts the angular momentum of the vortex by k \frac{{\tilde q}}{q}, where \tilde q is the electric charge of the quantum state of the vortex and q is the charge of the vortex scalar field under the U(1) gauge field. We also show that, for charged-particle-vortex composites angular momentum eigenvalues shift by k \frac{{\tilde q}}{q}, {\tilde q} being the electric charge of the charged-particle-vortex composite. This leads to the result that for \frac{{\tilde q}}{q} half-odd integral and for odd k our vertex operators flip the statistics of charged-particle-vortex composites from bosons to fermions and vice versa. For fractional values of \frac{{\tilde q}}{q}, application of vertex operator on charged-particle-vortex composite leads in general to composites with anyonic statistics.Comment: Published version, 15+1 pages, 1 figur

Algebraic characterization of anomalies in chiral WW_{3} gravity

The anomalies which occur in chiral WW_{3} gravity are characterized by solving the BRS consistency condition.Comment: 25 pages, report CBPF-NF-042/9