  Gauge fields associated with the manifestly covariant dynamics of particles
in $(3,1)$ spacetime are five-dimensional. In this paper we explore the old
problem of fields generated by a source undergoing hyperbolic motion in this
framework. The 5D fields are computed numerically using absolute time
$\tau$-retarded Green-functions, and qualitatively compared with Maxwell fields
generated by the same motion. We find that although the zero mode of all fields
coincides with the corresponding Maxwell problem, the non-zero mode should
affect, through the Lorentz force, the observed motion of test particles.
