Related papers: Deformed Carroll particle from 2+1 gravity
Point particles in 3D gravity are known to behave as topological defects, while gravitational field can be expressed as the Chern-Simons theory of the appropriate local isometry group of spacetime. In the case of the Poincar\'e group,…
With the exception of gravitation, the known fundamental interactions of Nature are mediated by gauge fields. A comparison of the candidate groups for a gauge theory possibly describing gravitation favours the Poincar\'e group as the…
Curved momentum spaces associated to the $\kappa$-deformation of the (3+1) de Sitter and Anti-de Sitter algebras are constructed as orbits of suitable actions of the dual Poisson-Lie group associated to the $\kappa$-deformation with…
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of kappa-deformations of the Poincare algebra with associated momenta living on (a…
Some special solutions of the Einstein-Maxwell action with a non-negative cosmological constant and a very heavy point mass particle have been obtained. The solutions correspond to static spacetime of locally constant curvature in its…
The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincare' gauge group symmetry by a…
The $\kappa$-deformation of the (2+1)D anti-de Sitter, Poincar\'e and de Sitter groups is presented through a unified approach in which the curvature of the spacetime (or the cosmological constant) is considered as an explicit parameter.…
We present an in-depth investigation of the ${\rm SL}(2,\mathbb{R})$ momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and…
We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and…
Quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions are revisited, and several features of these quantum structures are reviewed. In particular, the classification problem of (2+1) (A)dS Lie bialgebras is presented and the…
We present two different quantum deformations for the (anti)de Sitter algebras and groups. The former is a non-standard (triangular) deformation of SO(4,2) realized as the conformal group of the (3+1)D Minkowskian spacetime, while the…
A new derivation of the quantum deformation of the 2 dimensional Euclidean Poincare group (cf S. Zakrzewski) is proposed. It is based on a contraction of the Hopf algebra Fun(SO_q(3)). The deformation parameter q is sent to one, as in the…
Quantum field theories on de Sitter spacetime with global U(1) gauge symmetry are deformed using the joint action of the internal symmetry group and a one-parameter group of boosts. The resulting theory turns out to be wedge-local and…
All possible Drinfel'd double structures for the anti-de Sitter Lie algebra so(2,2) and de Sitter Lie algebra so(3,1) in (2+1)-dimensions are explicitly constructed and analysed in terms of a kinematical basis adapted to (2+1)-gravity. Each…
We present the generalisation to (3+1) dimensions of a quantum deformation of the (2+1) (Anti)-de Sitter and Poincar\'e Lie algebras that is compatible with the conditions imposed by the Chern-Simons formulation of (2+1) gravity. Since such…
We argue that the $\kappa$-deformation is related to a factorization of a Lie group, therefore {\em an approproate version of $\kappa$-Poincar\'{e} does exist on the $C^*$-algebraic level}. The explict form of this factorization is computed…
We present a new approach to the covariant canonical formulation of Einstein-Cartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from gravity in 2+1 dimensions regarding the…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
For theories formulated with a maximally symmetric momentum space we propose a general characterization for the description of interactions in terms of the isometry group of the momentum space. The well known cases of…
We construct quantum deformation of Poincar\'e group using as a starting point $SU(2,2)$ conformal group and twistor-like definition of the Minkowski space. We obtain quantum deformation of $SU(2,2)$ as a real form of multiparametric…