Green functions for wave propagation on a five-dimensional manifold and the associated gauge fields generated by a uniformly moving point source

Gauge fields associated with the manifestly covariant dynamics of particles in (3,1) space time are five dimensional (5D). We provide solutions of the classical 5D gauge field equations in both (4,1) and (3,2) flat space-time metrics for the simple example of a uniformly moving point source. Green functions for the 5D field equations are obtained, which are consistent with the solutions for uniform motion obtained directly from the field equations with free asymptotic conditions.