Abstract
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.
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Communicated by Raimar Wulkenhaar.
The author would like to thank Dorothea Bahns, André Fischer, Harald Grosse and Olaf Lechtenfeld for stimulating discussions and valuable comments.
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Zahn, J. Divergences in Quantum Field Theory on the Noncommutative Two-Dimensional Minkowski Space with Grosse–Wulkenhaar Potential. Ann. Henri Poincaré 12, 777–804 (2011). https://doi.org/10.1007/s00023-011-0089-0
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DOI: https://doi.org/10.1007/s00023-011-0089-0