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

Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential