Exploring Special Relative Locality with deSitter momentum-space

Abstract

Relative Locality is a recent approach to the quantum-gravity problem which allows to tame nonlocality effects which may rise in some models which try to describe Planck-scale physics. I here explore the effect of Relative Locality on basic special-relativistic phenomena. In particular I study the deformations due to Relative Locality of special-relativistic transformation laws for momenta at all orders in the rapidity parameter $\xi$. I underline how those transformations also define the RL characteristic (momentum-dependent) invariant metric. I focus my analysis on the well studied deSitter momentum-space framework and I investigate the differences and similarities between this model and Special Relativity, from the definition of the boost parameter $\gamma$ to a first discussion of transverse-effects characteristic of Relative Locality on clocks observables.

arXiv comment9 pages, 2 figures

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• Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
• Constraints on the deformation scale of a geometry in the cotangent bundle
• Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations
• Does a deformation of special relativity imply energy dependent photon time delays?
• Phenomenological Effects of CPT and Lorentz Invariance Violation in Particle and Astroparticle Physics
• Quantum-gravity-induced dual lensing and IceCube neutrinos
• Rainbow-like Black Hole metric from Loop Quantum Gravity
• Dispersion relations in finite-boost DSR
• Bounds on Relativistic Deformed Kinematics from the Physics of the Universe Transparency
• Time delays, choice of energy-momentum variables and relative locality in doubly special relativity
• DSR-relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation
• The universe is not a Lie, but actually an Hopf, algebra