The two-dimensional, \(N=2\) Wess-Zumino model on a cylinder (Q1113385)

We construct a family of supersymmetric, two-dimensional quantum field models. We establish the existence of the Hamiltonian H and the supercharge Q 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 by the authors [ibid. 112, 75-88 (1987; Zbl 0629.58040)] we establish an index theorem for Q, an infinite dimensional Dirac operator on loop space. This paper and, another related one by the first and the second authors [ibid. 114, 553-575 (1988; Zbl 0662.35095)] provide the technical justification for our claim and Q is Fredholm, and for our computation of its index by a homotopy onto quantum mechanics.