  We present a simple renormalizable abelian gauge model which includes
antisymmetric second-rank tensor fields as matter fields rather than gauge
fields known for a long time. The free action is conformally rather than gauge
invariant. The quantization of the free fields is analyzed and the one-loop
renormalization-group functions are evaluated. Transverse free waves are found
to convey no energy. The coupling constant of the axial-vector abelian gauge
interaction exhibits asymptotically free ultraviolet behavior, while the
self-couplings of the tensor fields do not asymptotically diminish.
