Dispersion relations in finite-boost DSR

Abstract

We find finite-boost transformations DSR theories in first order of the Planck length $l_p$, by solving differential equations for the modified generators. We obtain corresponding dispersion relations for these transformations, which help us classify the DSR theories via four types. The final type of our classification has the same special relativistic dispersion relation but the transformations are not Lorentz. In DSR theories, the velocity of photons is generally different from the ordinary speed c and possess time delay, however in this new DSR light has the same special relativistic speed with no delay. A special case demonstrates that any search for quantum gravity effects in observations which gives a special relativistic dispersion relation is consistent with DSR.

arXiv comment22 pages

References in corpus (31)

• Potential Sensitivity of Gamma-Ray Burster Observations to Wave Dispersion in Vacuo
• 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
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Minimal Length Scale Scenarios for Quantum Gravity
• Quantum Spacetime Phenomenology
• Generalized Lorentz invariance with an invariant energy scale
• Testing Einstein's special relativity with Fermi's short hard gamma-ray burst GRB090510
• Generalized Uncertainty Principle: Approaches and Applications
• Non-commutative space-time of Doubly Special Relativity theories
• Deformed Boost Transformations That Saturate at the Planck Scale
• Review on Generalized Uncertainty Principle
• Quantum-Gravity Analysis of Gamma-Ray Bursts using Wavelets
• Search for Lorentz Invariance breaking with a likelihood fit of the PKS 2155-304 flare data taken on MJD 53944
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• The Proton Spin and the Wigner Rotation
• Bounds on an energy-dependent and observer-independent speed of light from violations of locality
• Robust Constraint on Lorentz Violation Using Fermi-LAT Gamma-Ray Burst Data
• Improved limits on Lorentz invariance violation from astrophysical gamma-ray sources
• On the fate of Lorentz symmetry in relative-locality momentum spaces
• Relativistic kinematics beyond Special Relativity
• Consistent Lorentz violation features from near-TeV IceCube neutrinos
• Model-independent constraints on Lorentz invariance violation: implication from updated Gamma-ray burst observations
• Exploring Special Relative Locality with deSitter momentum-space
• Comparison of relativity theories with observer-independent scales of both velocity and length/mass
• Vector-like deformations of relativistic quantum phase-space and relativistic kinematics
• A Projective Interpretation of Some Doubly Special Relativity Theories
• Generalized relativistic kinematics in Poincaré-invariant models
• Dual DSR
• Dual Kappa Poincare Algebra

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• 5-Dimensional $SO(1,4)$-Invariant Action as an Origin to the Magueijo-Smolin Doubly Special Relativity Proposal
• DSR-relativistic spacetime picture and the phenomenology of Planck-scale-modified time dilation
• A winding number analysis of Schwarzschild black hole stability in light of Planck-scale modified kinematics