  We calculate divergent one-loop corrections to the propagators of the U(1)
gauge theory on the truncated Heisenberg space, which is one of the extensions
of the Grosse-Wulkenhaar model. The model is purely geometric, based on the
Yang-Mills action; the corresponding gauge-fixed theory is BRST invariant. We
quantize perturbatively and, along with the usual wave-function and mass
renormalizations, we find divergent nonlocal terms of the $\Box^{-1}$ and
$\Box^{-2}$ type. We discuss the meaning of these terms and possible
improvements of the model.
