  Inspired by the renormalizability of the non-commutative Phi^4 model with
added oscillator term, we formulate a non-commutative gauge theory, where the
oscillator enters as a gauge fixing term in a BRST invariant manner. All
propagators turn out to be essentially given by the Mehler kernel and the
bilinear part of the action is invariant under the Langmann-Szabo duality. The
model is a promising candidate for a renormalizable non-commutative U(1) gauge
theory.
