Scalar field propagation in the phi^4 kappa-Minkowski model
  In this article we use the noncommutative (NC) kappa-Minkowski phi^4 model based on the kappa-deformed star product, ({*}_h). The action is modified by expanding up to linear order in the kappa-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 kappa-Minkowski is specifically kappa-deformed. Thus our prescription in fact represents hybrid approach between standard quantum field theory (QFT) and NCQFT on the kappa-deformed Minkowski spacetime, resulting in a kappa-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 kappa-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 Planckian energies we obtain the direction dependent kappa-modified dispersion relations. Thus our kappa-effective model for the massive scalar field shows a birefringence effect. 
S. Meljanac, A. Samsarov, J. Trampetic and M. Wohlgenannt
hep-th gr-qc hep-ph