, Volume 12, Issue 4, pp 777-804
Date: 25 Feb 2011

Divergences in Quantum Field Theory on the Noncommutative Two-Dimensional Minkowski Space with Grosse–Wulkenhaar Potential

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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.

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.