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Scalar field propagation in the ϕ 4 κ-Minkowski model

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Abstract

In this article we use the noncommutative (NC) κ-Minkowski ϕ 4 model based on the κ-deformed star product, (★ h ). The action is modified by expanding up to linear order in the κ-deformation parameter a, producing an effective model on commutative spacetime. For the computation of the tadpole diagram contributions to the scalar field propagation/self-energy, we anticipate that statistics on the κ-Minkowski is specifically κ-deformed. Thus our prescription in fact represents hybrid approach between standard quantum field theory (QFT) and NCQFT on the κ-deformed Minkowski spacetime, resulting in a κ-effective model. The propagation is analyzed in the framework of the two-point Green’s function for low, intermediate, and for the Planckian propagation energies, respectively. Semiclassical/hybrid behavior of the first order quantum correction do show up due to the κ-deformed momentum conservation law. For low energies, the dependence of the tadpole contribution on the deformation parameter a drops out completely, while for Planckian energies, it tends to a fixed finite value. The mass term of the scalar field is shifted and these shifts are very different at different propagation energies. At the Planck-ian energies we obtain the direction dependent κ-modified dispersion relations. Thus our κ-effective model for the massive scalar field shows a birefringence effect.

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Authors and Affiliations

  1. Rudjer Bošković Institute, P.O.Box 180, HR-10002, Zagreb, Croatia

    S. Meljanac, A. Samsarov & J. Trampetić

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

    J. Trampetić

  3. Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090, Vienna, Austria

    M. Wohlgenannt

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  1. S. Meljanac
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Meljanac, S., Samsarov, A., Trampetić, J. et al. Scalar field propagation in the ϕ 4 κ-Minkowski model. J. High Energ. Phys. 2011, 10 (2011). https://doi.org/10.1007/JHEP12(2011)010

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