Relativistic deformed kinematics from momentum space geometry

Abstract

We present a way to derive a deformation of special relativistic kinematics (possible low energy signal of a quantum theory of gravity) from the geometry of a maximally symmetric curved momentum space. The deformed kinematics is fixed (up to change of coordinates in the momentum variables) by the algebra of isometries of the metric in momentum space. In particular, the well-known example of $\kappa$-Poincaré kinematics is obtained when one considers an isotropic metric in de Sitter momentum space such that translations are a subgroup of the isometry group, and for a Lorentz covariant algebra one gets the also well-known case of Snyder kinematics. We prove that our construction gives generically a relativistic kinematics and explain how it relates to previous attempts of connecting a deformed kinematics with a geometry in momentum space.

arXiv comment11 pages, no figures, final preprint version of the work published in PRD

References in corpus (15)

• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Quantum Spacetime Phenomenology
• The principle of relative locality
• String Theory and the Path to Unification: A Review of Recent Developments
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• A brief review of "little string theories"
• De Sitter space as an arena for Doubly Special Relativity
• Relative locality: A deepening of the relativity principle
• String theory: a perspective over the last 25 years
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Discrete Gravity Models and Loop Quantum Gravity: a Short Review
• Causal Sets: Quantum gravity from a fundamentally discrete spacetime
• Geometric interpretation of Planck-scale-deformed co-products
• Beyond Special Relativity at second order
• Snyder Momentum Space in Relative Locality

Cited by in corpus (38)

• Generalized uncertainty principle or curved momentum space?
• Phenomenological consequences of a geometry in the cotangent bundle
• Deformed relativistic kinematics on curved spacetime -- a geometric approach
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Constraints on the deformation scale of a geometry in the cotangent bundle
• Interplay between spacetime curvature, speed of light and quantum deformations of relativistic symmetries
• Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Relativistic Extended Uncertainty Principle from Spacetime Curvature
• Observables from spherically symmetric modified dispersion relations
• Spacetime and deformations of special relativistic kinematics
• Casimir effect in Snyder Space
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Reinterpreting deformed Heisenberg algebras
• Relativistic deformed kinematics from locality conditions in a generalized spacetime
• Two-body decays in deformed relativity
• Modification of the mean free path of very high energy photons due to a relativistic deformed kinematics
• Time delays, choice of energy-momentum variables and relative locality in doubly special relativity
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Relativistic deformed kinematics: from flat to curved spacetimes
• Space-time thermodynamics in momentum dependent geometries
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• A new perspective on Doubly Special Relativity
• Particle-antiparticle asymmetry in a relativistic deformed kinematics
• Doubly special relativity as a non-local quantum field theory
• Momentum gauge fields from curved momentum space through Kaluza-Klein reduction
• Covariant dynamics on the momentum space
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Fate of $\kappa$-Minkowski space-time in non-relativistic (Galilean) and ultra-relativistic (Carrollian) regimes
• Exploring black hole mechanics in cotangent bundle geometries
• Cosmic Neutrinos as a Window to Departures from Special Relativity
• Non-local quantum field theory from doubly special relativity
• Towards quantum Mechanics on the curved cotangent bundle
• Universal Horizons without Hypersurface Orthogonality
• Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity
• Statistical physics on Euclidean Snyder space: connections with the GUP and cosmological implications
• The universe is not a Lie, but actually an Hopf, algebra
• Kinetic gases in static spherically symmetric modified dispersion relations