In order to improve the problems of four-dimensional quantum field
theory it was suggested to include "gravity effects" through
quantizing space-time. The canonical deformation is particularly
simple, but the resulting models suffer from the UV/IR-mixing.
We found a way to handle this problem and obtain a renormalizable model
for which the Landau problem is solved. At the self duality point it is
almost solvable.
We point out that these models fulfill the wedge locality property.
