HILBERT-SPACE REPRESENTATIONS OF THE GAUGE GROUPS OF SOME 2-DIMENSIONAL FIELD-THEORIES

In this paper we show how the representation theory of gauge groups de veloped in [7] and [8] to study the massless Thirring model and repres entations of affine Lie algebras may be applied to the Schwinger model and to diagonal QCD2. We also discusss how this sheds light on the cu rrently unsolved problem of QCD2 itself. We show how to construct oper ators which approximate the quantum fields of the respective models on Hilbert space, how to represent the local gauge groups by unitary ope rators, positivity of the n-point functions in a definite metric quant isation and how to determine the observables and vacuum structure. Thi s analysis counterpoints the related work in [17] on the indefinite me tric version of the Schwinger model.