Exact Solution of the Sommerfeld Half-Plane Problem: a Path Integral Approach Without Discretization

Abstract

The exact solution of the two-dimensional Sommerfeld half-plane problem is obtained with a path integral approach. The approach relies on the Riemann space associated with this problem but does not require discretization nor a transformation to the corresponding heat conduction problem. A new intrinsic symmetry property of the half-plane problem solutions is revealed and is connected to the characteristics of the underlying Riemann space. An endpoint rather than a stationary point argument reproduces Keller's GTD results from the path integral expression.