Green Functions For Wave Propagation on a 5D 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) spacetime are five-dimensional. We provide solutions of the classical 5D gauge field equations in both (4,1) and (3,2) flat spacetime 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. 
I. Aharonovich, L. P. Horwitz