Geometric interpretation of Planck-scale-deformed co-products

Abstract

For theories formulated with a maximally symmetric momentum space we propose a general characterization for the description of interactions in terms of the isometry group of the momentum space. The well known cases of $\kappa$-Poincaré-inspired and (2+1)-dimensional gravity-inspired composition laws both satisfy our condition. Future applications might include the proposal of a class of models based on momenta spaces with anti-de Sitter geometry.

arXiv comment9 pages, Contribution to the proceedings of the 9th Alexander Friedmann International Seminar, St. Petersburg, Russia, June 21-27, 2015

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• Phenomenological consequences of a geometry in the cotangent bundle
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Constraints on the deformation scale of a geometry in the cotangent bundle
• Curved momentum space, locality, and generalized space-time
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Observables from spherically symmetric modified dispersion relations
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Space-time thermodynamics in momentum dependent geometries
• Relativistic deformed kinematics: from flat to curved spacetimes
• Particle-antiparticle asymmetry in a relativistic deformed kinematics
• Exploring black hole mechanics in cotangent bundle geometries
• Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity
• Kinetic gases in static spherically symmetric modified dispersion relations