Planck-scale modified dispersion relations and Finsler geometry

Abstract

A common feature of all Quantum Gravity (QG) phenomenology approaches is to consider a modification of the mass shell condition of the relativistic particle to take into account quantum gravitational effects. The framework for such approaches is therefore usually set up in the cotangent bundle (phase space). However it was recently proposed that this phenomenology could be associated with an energy dependent geometry that has been coined ``rainbow metric". We show here that the latter actually corresponds to a Finsler Geometry, the natural generalization of Riemannian Geometry. We provide in this way a new and rigorous framework to study the geometrical structure possibly arising in the semiclassical regime of QG. We further investigate the symmetries in this new context and discuss their role in alternative scenarios like Lorentz violation in emergent spacetimes or Deformed Special Relativity-like models.

Replaced with the published version

References in corpus (1)

• A Lagrangian for DSR Particle and the Role of Noncommutativity

Cited by in corpus (12)

• The General Very Special Relativity in Finsler Cosmology
• Modified (A)dS Schwarzschild black holes in Rainbow spacetime
• Lorentz Invariance Violation and Symmetry in Randers--Finsler Spaces
• Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
• The Higgs mechanism in Finsler spacetimes
• Propagation of light in area metric backgrounds
• Doubly Special Relativity and Finsler geometry
• Lorentz Invariance Violation from String Theory
• Foundations of anisotropic relativistic mechanics
• Rapidities and Observable 3-Velocities in the Flat Finslerian Event Space with Entirely Broken 3D Isotropy
• A note on particle kinematics in Horava-Lifshitz scenarios
• Remarks on DSR and Gravity