  In this note we investigate a new type of non-commutative field theory based
on a constant skew-symmetric three-form parameter. In 3+1 dimensions such a
three-form parameter can be viewed as a short-distance regulator which
nevertheless preserves spatial-rotation and at long range preserves Lorentz
invariance approximately. For a scalar field theory with quartic
self-interaction we obtain drastically improved ultra-violet behavior of the
diagrams, due to the oscillatory dependence of the interaction vertex on the
momenta. The radiative corrections to the coupling are rendered finite already
at the one-loop level. The key finding of this paper is that what appears as
the reemergence of UV divergences as IR singularity in $p \to 0$ limit, must be
interpreted simply as the logarithmic running of the coupling. Thus at low
energies the theory is virtually indistinguishable from the standard theory.
Conversely at high energies the diagram converges exponentially fast, the
running of the coupling stops and the theory avoids developing the Landau pole.
Bare coupling defined at high energy can be kept small, and in this sense the
theory is similar to asymptotically free theories.
