The two-dimensional,N=2 Wess-Zumino model on a cylinder

We construct a family of supersymmetric, two-dimensional quantum field models. We establish the existence of the HamiltonianH and the superchargeQ as self-adjoint operators. We establish the ultraviolet finiteness of the model, independent of perturbation theory. We develop functional integral representations of the heat kernel which are useful for proving estimates in these models. In a companion paper 1] we establish an index theorem forQ, an infinite dimensional Dirac operator on loop space. This paper and, another related one 2], provide the technical justification for our claim thatQ is Fredholm, and for our computation of its index by a homotopy onto quantum mechanics.Supported in part by the National Science Foundation under Grant DMS/PHY 86-45122Hertz Foundation Graduate Fellow