Doubly-Special Relativity: Facts, Myths and Some Key Open Issues

Abstract

I report, emphasizing some key open issues and some aspects that are particularly relevant for phenomenology, on the status of the development of "doubly-special" relativistic ("DSR") theories with both an observer-independent high-velocity scale and an observer-independent small-length/large-momentum scale, possibly relevant for the Planck-scale/quantum-gravity realm. I also give a true/false characterization of the structure of these theories. In particular, I discuss a DSR scenario without modification of the energy-momentum dispersion relation and without the $\kappa$-Poincaré Hopf algebra, a scenario with deformed Poincaré symmetries which is not a DSR scenario, some scenarios with both an invariant length scale and an invariant velocity scale which are not DSR scenarios, and a DSR scenario in which it is easy to verify that some observable relativistic (but non-special-relativistic) features are insensitive to possible nonlinear redefinitions of symmetry generators.

This is the preprint version of a paper prepared for a special issue "Feature Papers: Symmetry Concepts and Applications" of the journal Symmetry

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• Particle Dynamics on Snyder space
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Constraints on Lorentz Invariance and CPT Violation using Optical Photometry and Polarimetry of Active Galaxies BL Lacertae and S5 B0716+714
• Experimental Search for Quantum Gravity
• A Projective Interpretation of Some Doubly Special Relativity Theories
• Local free-fall Temperature of modified Schwarzschild black hole in rainbow spacetime
• Minimal-length quantum field theory: a first-principle approach
• On the depth of quantum space
• Lorentz violation, vacuum, cosmic rays, superbradyons and Pamir data
• Constraints on General Relativity Geodesics by a Covariant Geometric Uncertainty Principle
• Covariant Space Time Line Elements in the Friedmann Lemaitre Robertson Walker Geometry
• Thermodynamic analysis of a compact object in Rastall-Rainbow gravity