  In a rigorous construction of the path integral for supersymmetric quantum
mechanics on a Riemann manifold, based on B\"ar and Pf\"affle's use of
piecewise geodesic paths, the kernel of the time evolution operator is the heat
kernel for the Laplacian on forms. The path integral is approximated by the
integral of a form on the space of piecewise geodesic paths which is the
pullback by a natural section of Mathai and Quillen's Thom form of a bundle
over this space.
  In the case of closed paths, the bundle is the tangent space to the space of
geodesic paths, and the integral of this form passes in the limit to the
supertrace of the heat kernel.
