Path integral solution of linear second order partial differential equations I: the general construction
Copyright policy )Path integral solution of linear second order partial differential equations I: the general construction
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
linear second order partial differential equation, functional integration, Path integrals in quantum mechanics, Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.), FOS: Physical sciences, Mathematical Physics (math-ph), Partial differential equations, path integral, Mathematical Physics
linear second order partial differential equation, functional integration, Path integrals in quantum mechanics, Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.), FOS: Physical sciences, Mathematical Physics (math-ph), Partial differential equations, path integral, Mathematical Physics
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