Symmetries of quantum space-time in 3 dimensions

Abstract

By applying loop quantum gravity techniques to 3D gravity with a positive cosmological constant $\Lambda$, we show how the local gauge symmetry of the theory, encoded in the constraint algebra, acquires the quantum group structure of $s{o}_q(4)$, with $q=\exp (i\hslash \sqrt{\Lambda }/2\kappa )$. By means of an Inonu-Wigner contraction of the quantum group bi-algebra, keeping $\kappa$ finite, we obtain the kappa-Poincaré algebra of the flat quantum space-time symmetries.

In V2 some clarifying comments and references have been added according to the refereed version for Phys.Rev.D; in V3 we corrected the format of one figure

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Cited by in corpus (33)

• The loop gravity string
• Hypersurface-deformation algebroids and effective space-time models
• The kappa-(A)dS quantum algebra in (3+1) dimensions
• $\kappa$-deformed complex fields and discrete symmetries
• Testing Noncommutative Spacetimes and Violations of the Pauli Exclusion Principle with underground experiments
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• Strongest atomic physics bounds on Non-Commutative Quantum Gravity Models
• Constraining the loop quantum gravity parameter space from phenomenology
• Relativistic compatibility of the interacting $\kappa$-Poincaré model and implications for the relative locality framework
• Spectral dimension with deformed spacetime signature
• Experimental test of Non-Commutative Quantum Gravity by VIP-2 Lead
• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• A short introduction to $\kappa$-deformation
• Quantum $D=3$ Euclidean and Poincaré symmetries from contraction limits
• Extending general covariance: Moyal-type noncommutative manifolds
• $\kappa$-de Sitter and $\kappa$-Poincaré symmetries emerging from Chern-Simons (2+1)D gravity with a cosmological constant
• Quantizations of D=3 Lorentz symmetry
• Effective Chern-Simons actions of particles coupled to 3D gravity
• $\kappa$-deformed BMS symmetry
• Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic ${\mathfrak{o}}^{\star }(4)$ symmetries
• On the emergence of a classical Isotropic Universe from a Quantum $f(R)$ Bianchi Cosmology in the Jordan Frame
• Conformal quantum mechanics and holography in noncommutative space-time
• BMS algebras in 4 and 3 dimensions, their quantum deformations and duals
• Spinning Toroidal Brane Cosmology; A Classical and Quantum Survey
• $\kappa$-deformed power spectrum and modified Unruh temperature
• Quantum Klein Space and Superspace
• How does Casimir energy fall in $\kappa$-deformed space-time?
• Centripetal force on Casimir energies in $\kappa$-deformed rotating frame
• Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity
• Entropic force and bouncing behaviour in $\kappa$-Minkowski space-time
• Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes
• 3-dimensional $\Lambda$-BMS Symmetry and its Deformations
• Thermal Casimir effect in $\kappa$-Minkowski space-time