Doubly Special Relativity and Finsler geometry

Abstract

We discuss the recent proposal of implementing Doubly Special Relativity in configuration space by means of Finsler geometry. Although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give a complete description of the physics. In particular, the Finsler line element is not invariant under the deformed Lorentz transformations of Doubly Special Relativity. We study in detail some simple applications of the formalism.

8 pages, plain TeX

References in corpus (13)

• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Testable scenario for Relativity with minimum-length
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Planck-scale modified dispersion relations and Finsler geometry
• Non-Linear Relativity in Position Space
• Hopf-algebra description of noncommutative-spacetime symmetries
• A Lagrangian for DSR Particle and the Role of Noncommutativity
• The Free Particle in Deformed Special Relativity
• Transformations of coordinates and Hamiltonian formalism in deformed Special Relativity
• Planck-scale relativity from quantum $\kappa$-Poincaré algebra
• Position space versions of Magueijo-Smolin doubly special relativity proposal and the problem of total momentum
• A spacetime realization of kappa-Poincare algebra

Cited by in corpus (21)

• Principles of Einstein-Finsler Gravity and Perspectives in Modern Cosmology
• Realization of DSR-relativistic symmetries in Finsler geometries
• Geometry of physical dispersion relations
• Modified Dispersion Relations in Horava-Lifshitz Gravity and Finsler Brane Models
• Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
• Bi-metric pseudo-Finslerian spacetimes
• Pseudo-Finslerian spacetimes and multi-refringence
• Finsler Branes and Quantum Gravity Phenomenology with Lorentz Symmetry Violations
• Dual redshift on Planck-scale-curved momentum spaces
• Rainbows without unicorns: Metric structures in theories with Modified Dispersion Relations
• A Projective Interpretation of Some Doubly Special Relativity Theories
• Black Holes, Ellipsoids, and Nonlinear Waves in Pseudo-Finsler Spaces and Einstein Gravity
• Lorentz Violation in Finsler Geometry
• Aspects of General Relativity: Pseudo-Finsler extensions, Quasi-normal frequencies and Multiplication of tensorial distributions
• Five-Dimensional Mechanics as the Starting Point for the Magueijo-Smolin Doubly Special Relativity
• Nonholonomic Black Ring and Solitonic Solutions in Finsler and Extra Dimension Gravity Theories
• Wind-Finslerian structure of black holes
• Lifetime of flying particles in canonical Doubly Special Relativity
• DSR-relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation
• Principle action for particles faster than light
• Finslerian geometrodynamics