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Revisiting NCQED and scattering amplitudes

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Abstract

Research progress on the noncommutative gauge theories on the Moyal space is discussed in this minireview. We first present a brief overview on the development of gauge theories on Moyal space, with an emphasis on the role of Seiberg–Witten maps. Two important relations induced by reversible Seiberg–Witten maps, namely the formal equivalence of the on-shell DeWitt background field effective action in general and the explicit identical relation between tree-level scattering amplitudes in noncommutative quantum electrodynamics (NCQED), are described in some detail. We then proceed to the properties of the tree-level two-by-two scattering amplitudes in NCQED, including a forward scattering singularity in NCQED Compton scattering. After covering some phenomenological perspectives of noncommutative Yang–Mills (NCYM)-based models, outlooks for the future are given at the end.

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Data availability

The data sets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Notes

  1. The \(\star\)-product has also an alternative integral formulation, making its nonlocal character more transparent.

  2. We are particularly grateful to Peter Schupp for comments on the connection between SW maps and the Morita equivalence among star products and on the Kontsevich formality approach (see the next subsection).

  3. Note that UV/IR mixing is also connected to holography in a model-independent way [62] and nicely implemented into the idea of the scalar-field weak gravity conjecture, where it manifests as a form of hierarchical UV/IR mixing [63].

  4. We speculate that the answer to this question may be within/connected to the regularization of IR divergences in NCQED at loop levels, which is still unknown at this moment.

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Acknowledgements

J.T. thanks Dieter Lüst for many discussions and acknowledges the support of the Max-Planck-Institute for Physics, München, Germany, for hospitality.

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  1. Division of Experimental Physics, Ruđer Bošković Institute, Bijenička 54, 10000, Zagreb, Croatia

    Josip Trampetić

  2. Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, 80805, München, Germany

    Josip Trampetić

  3. Division of Physical Chemistry, Ruđer Bošković Institute, Bijenička 54, 10000, Zagreb, Croatia

    Jiangyang You

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Noncommutativity and Physics. Guest editors: George Zoupanos, Konstantinos Anagnostopoulos, Peter Schupp.

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Trampetić, J., You, J. Revisiting NCQED and scattering amplitudes. Eur. Phys. J. Spec. Top. 232, 3723–3731 (2023). https://doi.org/10.1140/epjs/s11734-023-00837-1

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