Exact solution of the sommerfeld half-plane problem: a path integral approach without discretization

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.