Quantum $\kappa$-Poincaré Algebra from de Sitter Space of Momenta

Abstract

There is a growing number of physical models, like point particle(s) in 2+1 gravity or Doubly Special Relativity, in which the space of momenta is curved, de Sitter space. We show that for such models the algebra of space-time symmetries possesses a natural Hopf algebra structure. It turns out that this algebra is just the quantum $\kappa$-Poincaré algebra.

arXiv comment10 pages

References in corpus (10)

• Lorentz invariance with an invariant energy scale
• Testable scenario for Relativity with minimum-length
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• 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
• Quantum symmetry, the cosmological constant and Planck scale phenomenology
• Observer-independent quanta of mass and length
• 2+1 gravity and Doubly Special Relativity
• Phase spaces of Doubly Special Relativity

Cited by in corpus (5)

• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• Blackbody radiation in κ-Minkowski spacetime
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications
• Snyder Space-Time: K-Loop and Lie Triple System