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

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

2004-05-10

arxiv.org/abs/math-ph/0405032v1

Physics

Mathematical Physics

33 pages

Scientific paper

10.1016/j.aop.2004.06.005

A theorem that constructs a path integral solution for general second order partial differential equations 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.

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