EQUIVALENCE OF 2-DIMENSIONAL QCD AND THE C = 1 MATRIX MODEL

We consider two-dimensional QCD with the spatial dimension compactifie d to a circle. We show that the states in the theory consist of intera cting strings that wind around the circle and derive the Hamiltonian f or this theory in the large N limit, complete with interactions. Mappi ng the winding states into momentum states, we express this Hamiltonia n in terms of a continuous field. For a U(N) gauge group with a backgr ound source of Wilson loops, we recover the collective field Hamiltoni an found by Das and Jevicki for the c = 1 matrix model, except the spa tial coordinate is on a circle. We then proceed to show that two-dimen sional QCD with a U(N) gauge group can be reduced to a one-dimensional unitary matrix model and is hence equivalent to a theory of N free no nrelativistic fermions on a circle. A similar result is true for the g roup SU (N), but the fermions must be modded out by the center of mass coordinate.