Geometry, Heat Equation and Path Integrals on the Poincare Upper Half-Plane

摘要

Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation delta f/delta t = delta /sub H/f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's proof that Feynman's path integral satisfies the Schroedinger equation is also valid for our case. (ERA citation 13:016934)