A Rigorous Path Integral for N=1 Supersymmetic Quantum Mechanics on a\n Riemannian Manifold

Following Feynman's prescription for constructing a path integral\nrepresentation of the propagator of a quantum theory, a short-time\napproximation to the propagator for imaginary time, N=1 supersymmetric quantum\nmechanics on a compact, even-dimensional Riemannian manifold is constructed.\nThe path integral is interpreted as the limit of products, determined by a\npartition of a finite time interval, of this approximate propagator. The limit\nunder refinements of the partition is shown to converge uniformly to the heat\nkernel for the Laplace-Beltrami operator on forms. A version of the steepest\ndescent approximation to the path integral is obtained, and shown to give the\nexpected short-time behavior of the supertrace of the heat kernel.\n