Matthias Ludewig
Given a parameter-dependent integral of the form $\int_M e^{-\phi(x)/2t} a(x) dx$ on a Riemannian manifold, it has an asymptotic expansion for small times, which can be calculated using the Laplace method. We then discuss a heuristic, infinite-dimensional version of the Laplace-method that can be used to formally associate an asymptotic expansion to path integrals, i.e. integrals over infinite-dimensional domains. Finally, we show how parts of it can be made rigorous using finite-dimensional approximation methods.
