Path Integral Solution of Linear Second Order Partial Differential Equations I. The General Construction

Abstract

A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schrödinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette.

40 pages

References in corpus (2)

• ${\delta }^{\prime }$-Function Perturbations and Neumann Boundary-Conditions by Path Integration
• Path Integral Discussion of Two and- Three-Dimensional $\delta$-Function Perturbations

Cited by in corpus (1)

• Path Integral Solution of Linear Second Order Partial Differential Equations II. Elliptic, Parabolic and Hyperbolic Cases