We consider the issue of statistics for identical particles or fields in $\kappa$-deformed spaces, where the system admits a symmetry group $G$. We obtain the twisted flip operator compatible with the action of the symmetry group, which is relevant for describing particle statistics in the presence of the noncommutativity. It is shown that for a special class of realizations, the twisted flip operator is independent of the ordering prescription.

In this paper, we study the deformed statistics and oscillator algebras of quantum fields defined in $\kappa$-Minkowski spacetime. The twisted flip operator obtained from the twist associated with the star product requires an enlargement of the Poincaré algebra to include the dilatation generators. Here we propose a novel notion of a fully covariant flip operator and show that to the first order in the deformation parameter it can be expressed completely in terms of the Poincaré generators alone. The $R$ matrices corresponding to the twisted and the covariant flip operators are compared up to first order in the deformation parameter and they are shown to be different. We also construct the deformed algebra of the creation and annihilation operators that arise in the mode expansion of a scalar field in $\kappa$-Minkowski spacetime. We obtain a large class of such new deformed algebras which, for certain choice of realizations, reduce to results known in the literature.

We consider simple extensions of noncommutativity from flat to curved spacetime. One possibility is to have a generalization of the Moyal product with a covariantly constant noncommutative tensor $\theta^{\mu\nu}$. In this case the spacetime symmetry is restricted to volume preserving diffeomorphisms which also preserve $\theta^{\mu\nu}$. Another possibility is an extension of the Kontsevich product to curved spacetime. In both cases the noncommutative product is nonassociative. We find the the order $\theta^2$ noncommutative correction to the Newtonian potential in the case of a covariantly constant $\theta^{\mu\nu}$. It is still of the form $1/r$ plus an angle dependent piece. The coupling to matter gives rise to a propagator which is $\theta$ dependent.

In this paper, we derive Lorentz force and Maxwell’s equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to noncommutative space-time. We also show the equivalence of minimal coupling prescription and Feynman’s approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this noncommutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.

In this paper, we derive corrections to the geodesic equation due to the $\kappa$-deformation of curved spacetime, up to the first order in the deformation parameter $a$. This is done by generalizing the method from our previous paper [ Phys. Rev. D 84, 085020 (2011)] to include curvature effects. We show that the effect of $\kappa$-noncommutativity can be interpreted as an extra drag that acts on the particle while moving in this $\kappa$-deformed curved spacetime. We have derived the Newtonian limit of the geodesic equation and using this, we discuss possible bounds on the deformation parameter. We also derive the generalized uncertainty relations valid in the nonrelativistic limit of the $\kappa$-spacetime.

We obtain an exact analytic expression for the quasinormal modes of a non-commutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the equations of motion governing these quasinormal modes are identical in form to the equations of motion of a commutative massive scalar field in the background of a fictitious massive spinning BTZ black hole. This results hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole. Using the obtained results for quasinormal mode frequencies, the area and entropy spectra for the BTZ black hole in the presence of noncommutativity are calculated. In particular, the separations between the neighboring values of these spectra are determined and it is found that they are nonuniform. Therefore, it appears that the noncommutativity leads to a non-equispaced (discrete) area and entropy spectra.