Related papers: Deformed Carroll particle from 2+1 gravity
In [1,2] we established and discussed the algebra of observables for $2+1$ gravity at both the classical and quantum level, and gave a systematic discussion of the reduction of the expected number of independent observables to $6g - 6 (g >…
We investigate the canonical quantization of gravity coupled to pointlike matter in 2+1 dimensions. Starting from the usual point particle action in the first order formalism, we introduce auxiliary variables which make the action locally…
The gauge theory of the de Sitter group, SO$(1,4)$, in the ambient space formalism has been considered in this article. This method is essential to constructing the de Sitter super-conformal gravity and Quantum gravity. $10$ gauge vector…
We make use of a well-know deformation of the Poincar\'e Lie algebra in $p+q+1$ dimensions ($p+q>0$) to construct the Poincar\'e Lie algebra out of the Lie algebras of the de Sitter and anti de Sitter groups, the generators of the…
We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…
In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…
Deformed special relativity is embedded in deformed general relativity using the methods of canonical relativity and loop quantum gravity. Phase-space dependent deformations of symmetry algebras then appear, which in some regimes can be…
The non-standard (Jordanian) quantum deformations of $so(2,2)$ and (2+1) Poincar\'e algebras are constructed by starting from a quantum $sl(2,\R)$ basis such that simple factorized expressions for their corresponding universal $R$-matrices…
We show how Wigner's little group approach to the representation theory of Poincar\'e group may be generalized to the case of $\kappa$-deformed Poincar\'e group. We also derive the deformed Lorentz transformations of energy and momentum. We…
We consider the operation of contraction of unitary irreducible representations of the de Sitter group $ SO(4,1) $. It is shown that a direct sum of unitary irreducible representations of the Poincar\'{e} group with different signs of the…
We present a simple algebraic argument for the conclusion that the low energy limit of a quantum theory of gravity must be a theory invariant, not under the Poincare group, but under a deformation of it parameterized by a dimensional…
We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincar\'e algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial…
We introduce a general framework for describing deformed phase spaces with group valued momenta. Using techniques from the theory of Poisson-Lie groups and Lie bi-algebras we develop tools for constructing Poisson structures on the deformed…
Particles propagating in de Sitter spacetime can be described by the topological BF $\SO(4,1)$ theory coupled to point charges. Gravitational interaction between them can be introduced by adding to the action a symmetry breaking term, which…
The problem of the gauge hierarchy is brought up in a hypercomplex scheme for a U(1) field theory; in such a scheme a compact gauge group is deformed through a \gamma-parameter that varies along a non-compact internal direction, transverse…
In this article, we quantize the Maxwell ("massless spin one") de Sitter field in a conformally invariant gauge. This quantization is invariant under the SO$_0(2,4)$ group and consequently under the de Sitter group. We obtain a new de…
We show that depending on the direction of deformation of $\kappa$-Poincar\'e algebra (time-like, space-like, or light-like) the associated phase spaces of single particle in Doubly Special Relativity theories have the energy-momentum…
We derive a scalar field theory of the deformed special relativity type, living on non-commutative kappa-Minkowski spacetime and with a kappa-deformed Poincare symmetry, from the SO(4,1) group field theory defining the transition amplitudes…
We discuss static particle-like solitons in the 2+1 dimensional CP(1) model with a small mass deformation $m$ preserving a $U(1) \times Z_2$ symmetry in the Lagrangian. Due to the breaking of scale invariance, the energy function becomes a…
We consider the physical implications of various choices of the three-momentum basis in the kappa-deformed Poincare algebra. In particular, we find that the energy dependence of the velocity of a kappa-particle leads to unexpected features…