Phase spaces of Doubly Special Relativity

Abstract

We show that depending on the direction of deformation of $\kappa$-Poincaré algebra (time-like, space-like, or light-like) the associated phase spaces of single particle in Doubly Special Relativity theories have the energy-momentum spaces of the form of de Sitter, anti-de Sitter, and flat space, respectively.

9 pages

References in corpus (20)

• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Generalized Lorentz invariance with an invariant energy scale
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Non-commutative space-time of Doubly Special Relativity theories
• Deformed Boost Transformations That Saturate at the Planck Scale
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Observer-independent quanta of mass and length
• Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
• De Sitter space as an arena for Doubly Special Relativity
• Doubly Special Relativity and de Sitter space
• 2+1 gravity and Doubly Special Relativity
• Quantum deformation of quantum gravity
• Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity
• The Kappa-Weyl group and its algebra
• Doubly Special Relativity with light-cone deformation
• Kappa-Deformed Phase Space and Uncertainty Relations

Cited by in corpus (22)

• Minimal Length Scale Scenarios for Quantum Gravity
• Quantum Spacetime Phenomenology
• Introduction to Doubly Special Relativity
• Charged BTZ black holes in the context of massive gravity's rainbow
• The Free Particle in Deformed Special Relativity
• Spacetime-noncommutativity regime of Loop Quantum Gravity
• DSR Relativistic Particle in a Lagrangian formulation and Non-Commutative Spacetime: A Gauge Independent Analysis
• Non-commutative relativistic spacetimes and worldlines from 2+1 quantum (anti-)de Sitter groups
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• Doubly Special Relativity as a Limit of Gravity
• $\kappa$-Poincaré-comodules, Braided Tensor Products and Noncommutative Quantum Field Theory
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Approaching Space Time Through Velocity in Doubly Special Relativity
• A note on DSR-like approach to space-time
• Quantum $\kappa$-Poincaré Algebra from de Sitter Space of Momenta
• Canonical, Lie-algebraic and quadratic twist deformations of Galilei group
• Equilibrium properties of blackbody radiation with an ultraviolet energy cut-off
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• The E(2) Particle
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• T-Minkowski noncommutative spacetimes I: Poincaré groups, differential calculi and braiding
• Doubly Special Relativity and quantum gravity phenomenology