Realization of DSR-relativistic symmetries in Finsler geometries

Abstract

Finsler geometry is a well known generalization of Riemannian geometry which allows to account for a possibly non trivial structure of the space of configurations of relativistic particles. We here establish a link between Finsler geometry and the sort of models with curved momentum space and DSR-relativistic symmetries which have been recently of interest in the quantum-gravity literature. We use as case study the much-studied scenario which is inspired by the $\kappa$-Poincaré quantum group, and show that the relevant deformation of relativistic symmetries can be implemented within a Finsler geometry.

References in corpus (8)

• Very Special Relativity
• General Very Special Relativity is Finsler Geometry
• Planck-scale modified dispersion relations and Finsler geometry
• Speed of particles and a relativity of locality in $\kappa$-Minkowski quantum spacetime
• Doubly Special Relativity and Finsler geometry
• Foundations of anisotropic relativistic mechanics
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• $\kappa$-Poincaré phase space: speed of massless particles and relativity of spacetime locality

Cited by in corpus (12)

• Investigation on Finsler geometry as a generalization to curved spacetime of Planck-scale-deformed relativity in the de Sitter case
• Deformed relativity symmetries and the local structure of spacetime
• Curved momentum spaces from quantum groups with cosmological constant
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Radar orthogonality and radar length in Finsler and metric spacetime geometry
• Phenomenological Effects of CPT and Lorentz Invariance Violation in Particle and Astroparticle Physics
• Affine sphere spacetimes which satisfy the relativity principle
• Relativistic deformed kinematics: from flat to curved spacetimes
• The extended phase space thermodynamics of Planck-scale-corrected Reissner-Nordström-anti-de Sitter black hole
• On axiomatic formulation of gravity and matter field theories with MDRs and Finsler-Lagrange-Hamilton geometry on (co)tangent Lorentz bundles
• Exploring black hole mechanics in cotangent bundle geometries
• Electromagnetic and gravitational interactions from Lagrangian mechanics