Path integral solution of linear second order partial differential equations II: elliptic, parabolic, and hyperbolic cases

Abstract

The general theorem of LaChapelle [Path Integral Solution of Linear Second Order Partial Differential Equations. I. The General Case, preprint (2003)] is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial differential equations with Dirichlet/Neumann boundary conditions. The construction is checked by evaluating several known kernels for regions with planar and spherical boundaries. Some new calculational techniques are introduced.