We compare two versions of deformed dispersion relations (energy vs momenta and momenta vs energy) and the corresponding time delay up to the second order accuracy in the quantum gravity scale (deformation parameter). A general framework describing modified dispersion relations and time delay with respect to different noncommutative kappa -Minkowski spacetime realizations is firstly proposed here and it covers all the cases introduced in the literature. It is shown that some of the realizations provide certain bounds on quadratic corrections, i.e. on quantum gravity scale, but it is not excluded in our framework that quantum gravity scale is the Planck scale. We also show how the coefficients in the dispersion relations can be obtained through a multiparameter fit of the gamma ray burst (GRB) data.
The $κ$-Minkoswki space-time provides a quantum noncommutative-deformation of the usual Minkowski space-time. However, a notion of causality is difficult to be defined in such a space with noncommutative time. In this paper, we define a notion of causality on a (1+1)-dimensional $κ$-Minkoswki space-time using the more general framework of Lorentzian noncommutative geometry. We show that this notion allows specific causal relations, but limited by a general constraint which is a quantum generalization of the traditional speed of light limit.
We consider the Lie group $\mathbb{R}^D_κ$ generated by the Lie algebra of $κ$-Minkowski space. Imposing the invariance of the metric under the pull-back of diffeomorphisms induced by right translations in the group, we show that a unique right invariant metric is associated with $\mathbb{R}^D_κ$. This metric coincides with the metric of de Sitter space-time. We analyze the structure of unitary representations of the group $\mathbb{R}^D_κ$ relevant for the realization of the non-commutative $κ$-Minkowski space by embedding into $(2D-1)$-dimensional Heisenberg algebra. Using a suitable set of g…
In this paper we have analyzed the $κ$-deformed Minkowski spacetime through the light of the interference phenomena in QFT where two opposite chiral fields are put together in the same multiplet and its consequences are discussed. The chiral models analyzed here are the chiral Schwinger model, its generalized version and its gauge invariant version, where a Wess-Zumino term were added. We will see that the final actions obtained here are in fact related to the original ones via duality transformations.
We construct a non-commutative kappa-Minkowski deformation of U(1) gauge theory, following a general approach, recently proposed in JHEP 2008 (2020) 041. We obtain an exact (all orders in the non-commutativity parameter) expression for both the deformed gauge transformations and the deformed field strength, which is covariant under these transformations. The corresponding Yang-Mills Lagrangian is gauge covariant and reproduces the Maxwell Lagrangian in the commutative limit. Gauge invariance of the action functional requires a non-trivial integration measure which, in the commutative limit, do…
In this paper, we analyze the Hawking radiation of a kappa-deformed Schwarzchild black hole and obtain the deformed Hawking temperature. For this, we first derive deformed metric for the kappa-spacetime, which in the generic case, is not a symmetric tensor and also has a momentum dependence. We show that the Schwarzchild metric obtained in the kappa-deformed spacetime has a dependence on energy. We use the fact that the deformed metric is conformally flat in the 1+1 dimensions, to solve the kappa-deformed Klein-Gordon equation in the background of the Schwarzchild metric. The method of Bogulio…
We recently constructed the $R$-Poincaré algebra from an appropriate deformed Poisson brackets which reproduce the Fock coordinate transformation. We showed then that the spacetime of this transformation is the de Sitter one. In this paper, we derive in the $R$-Minkowski spacetime the Dirac equation and show that this is none other than the Dirac equation in the de Sitter spacetime given by its conformally flat metric. Furthermore, we propose a new approach for solving Dirac's equation in the de Sitter spacetime using the Schrödinger picture.
In this short note, based on the talk given at the 3rd Conference of the Polish Society on Relativity, I present the basic points of our recent paper "Symmetries of quantum spacetime in three dimensions", stressing their physical meaning, and avoiding technical details.
We uncover an infinite number of vacua in two-dimensional quantum field theory, the Klein-Gordon field for simplicity, by conceiving a new mode that is classified by a real positive parameter $κ$. We show each mode has a distinct vacuum, say $κ$-vacuum. This new mode is a generalization of the Unruh-Minkowski mode. Moreover, the Minkowski and Rindler vacua are special cases of the $κ$-vacuum for $κ= 1$ and $κ\rightarrow \infty$, respectively.
We consider the $\varrho$-Minkowski spacetime, a model with linear noncommutativity involving the time and the azimuthal angle. We study its quantum symmetries, the $\varrho$-Poincaré quantum group, and analyse the concepts of localizability and quantum observers.
Using the methods of ordinary quantum mechanics we study $κ$-Minkowski space as a quantum space described by noncommuting self-adjoint operators, following and enlarging arXiv:1811.08409. We see how the role of Fourier transforms is played in this case by Mellin transforms. We briefly discuss the role of transformations and observers.
