Divergencies in a field theory on quantum space

We investigate field theories defined on spaces with non-commutative coordinates corresponding to deformations of flat spaces as e.g. the Euclidean plane or Minkowski space. When re-expressed in terms of ordinary complex fields, the interactions are non-local. Despite this fact, these field theories exhibit the same kind of divergencies as the non-deformed models, due to special graph-topological properties of cocylcles connected with the non-commutative coordinates.