Abstract
We study infrared divergences due to ultraviolet–infrared mixing in quantum field theory on Moyal space with Lorentzian signature in the Yang–Feldman formalism. Concretely, we are considering the \({\phi^4}\) and the \({\phi^3}\) model in arbitrary even dimension. It turns out that the situation is worse than in the Euclidean setting, in the sense that we find infrared divergences in graphs that are finite there. We briefly discuss the problems one faces when trying to adapt the nonlocal counterterms that render the Euclidean model renormalizable.
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Acknowledgments
It is a pleasure to thank Dorothea Bahns and Michał Wrochna for helpful discussions. This work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Göttingen.
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Communicated by Raimar Wulkenhaar.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Zahn, J. Ultraviolet–Infrared Mixing on the Noncommutative Minkowski Space in the Yang–Feldman Formalism. Ann. Henri Poincaré 13, 1271–1289 (2012). https://doi.org/10.1007/s00023-011-0153-9
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DOI: https://doi.org/10.1007/s00023-011-0153-9