  Let M be a compact Riemannian manifold without boundary and let H be a
self-adjoint generalized Laplace operator acting on sections in a bundle over
M. We give a path integral formula for the solution to the corresponding heat
equation. This is based on approximating path space by finite dimensional
spaces of geodesic polygons. We also show a uniform convergence result for the
heat kernels. This yields a simple and natural proof for the
Hess-Schrader-Uhlenbrock estimate and a path integral formula for the trace of
the heat operator.
