Canonical Realizations of Doubly Special Relativity
arXiv:gr-qc/0702027 · doi:10.1142/S0218271807010638
Abstract
Doubly Special Relativity is usually formulated in momentum space, providing the explicit nonlinear action of the Lorentz transformations that incorporates the deformation of boosts. Various proposals have appeared in the literature for the associated realization in position space. While some are based on noncommutative geometries, others respect the compatibility of the spacetime coordinates. Among the latter, there exist several proposals that invoke in different ways the completion of the Lorentz transformations into canonical ones in phase space. In this paper, the relationship between all these canonical proposals is clarified, showing that in fact they are equivalent. The generalized uncertainty principles emerging from these canonical realizations are also discussed in detail, studying the possibility of reaching regimes where the behavior of suitable position and momentum variables is classical, and explaining how one can reconstruct a canonical realization of doubly special relativity starting just from a basic set of commutators. In addition, the extension to general relativity is considered, investigating the kind of gravity's rainbow that arises from this canonical realization and comparing it with the gravity's rainbow formalism put forward by Magueijo and Smolin, which was obtained from a commutative but noncanonical realization in position space.
18 pages, accepted for publication in International Journal of Modern Physics D
References in corpus (27)
- Discreteness of area and volume in quantum gravity
- Quantum gravity and minimum length
- Lorentz invariance with an invariant energy scale
- Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
- Quantum Theory of Gravity I: Area Operators
- Testable scenario for Relativity with minimum-length
- Generalized Lorentz invariance with an invariant energy scale
- Gravity's Rainbow
- Doubly Special Relativity
- Lectures on Loop Quantum Gravity
- Doubly Special Relativity theories as different bases of --Poincaré algebra
- Deformed Boost Transformations That Saturate at the Planck Scale
- Quantum Uncertainty in Doubly Special Relativity
- Observer-independent quanta of mass and length
- Self-consistency in Theories with a Minimal Length
- Non-Linear Relativity in Position Space
- Conservation Laws in Doubly Special Relativity
- Quantum-Gravity Phenomenology: Status and Prospects
- 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
- Space-time quantum solves three experimental paradoxes
- Asymptotic Flatness in Rainbow Gravity
- Transformations of coordinates and Hamiltonian formalism in deformed Special Relativity
- On reaction thresholds in doubly special relativity
- Length Uncertainty in a Gravity's Rainbow Formalism
- Canonical DSR
Cited by in corpus (12)
- Quantum Spacetime Phenomenology
- 30 years in: Quo vadis generalized uncertainty principle?
- Rigorous Hamiltonian and Lagrangian analysis of classical and quantum theories with minimal length
- Generalized uncertainty principle or curved momentum space?
- About Locality and the Relativity Principle Beyond Special Relativity
- Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
- Time delay of light signals in an energy-dependent spacetime metric
- Space and time transformations with a minimal length
- Quantum Noncanonical Field Theory: Symmetries and Interaction
- DSR and Canonical Transformations: A Comment on a ``A Lagrangian for DSR particle and the role of noncommutativity''
- Lifetime of flying particles in canonical Doubly Special Relativity
- On the invariance of the relative rest in doubly special relativity