Path integrals, microlocal analysis and the fundamental solution for Hörmander Laplacians
Wolfgang Staubach · TSpace (University of Toronto) · 2003
In this thesis we present an explicit calculation of the heat kernel, fundamental solution and the Schwartz kernel of the resolvent for the Heisenberg Laplacian using Wiener path integrals and their realizations via Trotter product formula. This gives also another derivation of the Mehler's formula. We give a path integral formula for the heat kernel of some general higher step Hörmander Laplacians. We use also microlocal analysis, more explicitly the Weyl calculus of pseudodifferential operators to find the heat kernel for a model class of step 2 Hörmander Laplacians.