  Quantum field theory on the noncommutative two-dimensional Minkowski space
with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a
continuous set of generalised eigenfunctions of the wave operator, and directly
in position space. In both settings, we find a new type of divergence in planar
graphs. It is present at and above the self-dual point. This new kind of
divergence might make the construction of a Minkowski space version of the
Grosse-Wulkenhaar model impossible.
