Relative locality in κ-Poincaré

Abstract

Abstract. We show that the κ-Poincaré Hopf algebra can be interpreted in the framework of curved momentum space leading to relative locality. We study the geometric properties of the momentum space described by κ-Poincaré, and derive the consequences for particles propagation and energy-momentum conservation laws in interaction vertices, obtaining for the first time a coherent and fully workable model of the deformed relativistic kinematics implied by κ-Poincaré. We describe the action of boost transformations on multi-particle systems, showing that in order to keep covariant the composed momenta it is necessary to introduce a dependence of the rapidity parameter on the particles momenta themselves. Finally, we show that this particular form of the boost transformations keeps the validity of the relativity principle, demonstrating the invariance of the equations of motion under boost transformations.

Quantum statistics and noncommutative black holes

“…For this particular special class of ϕ-realizations, the twist element is given in (29). Using (29) and (35), we obtain an explicit expression for the twisted flip operator τ ϕ for the class of realizations ψ(A) = 1 as…”

“…Using (29) and (35), we obtain an explicit expression for the twisted flip operator τ ϕ for the class of realizations ψ(A) = 1 as…”

“…It also appears in the context of noncommutative FRW cosmologies [16]. In addition, the κ-Minkowski algebra is relevant in models of doubly-special relativity and in the analysis of astrophysical data from the GRB's [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. This wide-ranging appearance of the κ-cylinder algebra * kumars.gupta@saha.ac.in † meljanac@irb.hr ‡ asamsarov@irb.hr suggests that it captures certain generic features of noncommutative gravity and black holes and is therefore an interesting toy model to explore Planck scale physics.…”

Kinematics of particles with quantum-de Sitter-inspired symmetries

“…In this context, one of the most studied models is the one described by the κ-Poincaré Hopf algebra [21][22][23][24], a quantum deformation of the special-relativistic Poincaré group. κ-Poincaré symmetries have been shown to characterize the kinematics of particles living on a flat spacetime and nontrivial momentum space with a de Sitter geometry [25][26][27][28]. 1 Despite the fact that most of the research on relativistically compatible deformations of particles' kinematics focuses on cases where spacetime is flat, as mentioned before the best opportunities for phenomenology are found in contexts where spacetime curvature should not be neglected.…”

Geometric picture of DSR-relativistic theories with de Sitter and anti-de Sitter momentum spaces

“…For details, see Ref. 4 space-time and (2+1)-dimensional quantum-gravity can be related, respectively, to a de Sitter and an anti-de Sitter metric for the momentum space.…”