Deformed Special Relativity in Position Space
arXiv:gr-qc/0612167 · doi:10.1016/j.physletb.2007.04.019
Abstract
We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a parametrization in terms of an energy dependent speed of light, and an energy dependent Planck's constant, we are able to formulate simple requirements that completely determine the active transformations in position space. These deviate from the standard transformations for large velocities of the observed object. Some examples are discussed, and it is shown how the relativistic mass gain of a massive particle is affected. We finally study the construction of passive Lorentz-transformations.
replaced with published version. due to page limits this version is significantly shorter than the 1st
References in corpus (45)
- Hilbert Space Representation of the Minimal Length Uncertainty Relation
- Lorentz invariance with an invariant energy scale
- Testable scenario for Relativity with minimum-length
- Bicrossproduct structure of -Poincare group and non-commutative geometry
- Generalized Lorentz invariance with an invariant energy scale
- Gravity's Rainbow
- The algebraic structure of the generalized uncertainty principle
- Quantum Groups, Gravity, and the Generalized Uncertainty Principle
- Classical and Quantum Mechanics of Free \k Relativistic Systems
- Planck-scale deformation of Lorentz symmetry as a solution to the UHECR and the TeV- paradoxes
- Signatures in the Planck Regime
- Doubly-Special Relativity: First Results and Key Open Problems
- Doubly Special Relativity theories as different bases of --Poincaré algebra
- Deformed Boost Transformations That Saturate at the Planck Scale
- Robust Limits on Lorentz Violation from Gamma-Ray Bursts
- Observer-independent quanta of mass and length
- TeV Astrophysics Constraints on Planck Scale Lorentz Violation
- New limits on Planck scale Lorentz violation in QED
- Interpretation of Quantum Field Theories with a Minimal Length Scale
- Self-consistency in Theories with a Minimal Length
- Non-Linear Relativity in Position Space
- Observational Limits on Quantum Geometry Effects
- Conservation Laws in Doubly Special Relativity
- Quantum-Gravity Phenomenology: Status and Prospects
- Falsifiable predictions from semiclassical quantum gravity
- Loop Quantum Gravity and Ultra High Energy Cosmic Rays
- Entropy and temperature of black holes in a gravity's rainbow
- Possible astrophysical probes of quantum gravity
- Quantum Time Uncertainty in a Gravity's Rainbow Formalism
- The Free Particle in Deformed Special Relativity
- Asymptotic Flatness in Rainbow Gravity
- Interpreting doubly special relativity as a modified theory of measurement
- On the definition of velocity in doubly special relativity theories
- On reaction thresholds in doubly special relativity
- Could quantum gravity be tested with high intensity Lasers?
- Length Uncertainty in a Gravity's Rainbow Formalism
- Canonical DSR
- The kinematics of particles moving in rainbow spacetime
- Some Consequences of a Generalization to Heisenberg Algebra in Quantum Electrodynamics
- Building a case for a Planck-scale-deformed boost action: the Planck-scale particle-localization limit
- On the Lorentz Transformations of Momentum and Energy
- Doubly Special Relativity: A New Relativity or Not?
- Special relativity with two invariant scales: Motivation, Fermions, Bosons, Locality, and Critique
- Some comments on the universal constant in DSR
- A Field Theory Model With a New Lorentz-Invariant Energy Scale
Cited by in corpus (20)
- Minimal Length Scale Scenarios for Quantum Gravity
- Bounds on an energy-dependent and observer-independent speed of light from violations of locality
- Modified (A)dS Schwarzschild black holes in Rainbow spacetime
- The Big Bounce in Rainbow Universe
- Modified Dispersion Relations and Black Hole Entropy
- A Note on Quantum Field Theories with a Minimal Length Scale
- Generalized Uncertainty Principle Removes The Chandrasekhar Limit
- DSR as an explanation of cosmological structure
- The Soccer-Ball Problem
- Inertial frames without the relativity principle
- Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
- Gravity's rainbow: a bridge between LQC and DSR
- The Box-Problem in Deformed Special Relativity
- Deformed Special Relativity from Asymptotically Safe Gravity
- Time delay of light signals in an energy-dependent spacetime metric
- Influence of the dispersion relation on the Unruh effect according to the relativistic Doppler shift method
- Minimum Length - Maximum Velocity
- Lifetime of flying particles in canonical Doubly Special Relativity
- Local Lorentz Transformation and "Lorentz Violation"
- On the Meaning of Localization in Non-Local Quantum Field Theory