Triply Special Relativity

Abstract

We describe an extension of special relativity characterized by {\it three} invariant scales, the speed of light, $c$, a mass, $\kappa$ and a length $R$. This is defined by a non-linear extension of the Poincare algerbra, $\mathcal{A}$, which we describe here. For $R\to \infty$, $\mathcal{A}$ becomes the Snyder presentation of the $\kappa$-Poincare algebra, while for $\kappa \to \infty$ it becomes the phase space algebra of a particle in deSitter spacetime. We conjecture that the algebra is relevant for the low energy behavior of quantum gravity, with $\kappa$ taken to be the Planck mass, for the case of a nonzero cosmological constant $\Lambda =R^{-2}$. We study the modifications of particle motion which follow if the algebra is taken to define the Poisson structure of the phase space of a relativistic particle.

13 pages

References in corpus (1)

• Topological excitations around the vacuum of quantum gravity I: The symmetries of the vacuum

Cited by in corpus (62)

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• Thermodynamics of the Reissner-Nordström black hole with quintessence matter on the EGUP framework
• Doubly special relativity in de Sitter spacetime
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• Doubly Special Relativity in Position Space Starting from the Conformal Group
• Investigation of Unruh temperature of Black holes by using of EGUP formalism
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• Snyder dynamics in a Schwarzschild spacetime
• Classical dynamics on curved Snyder space
• Natural Cutoffs via Compact Symplectic Manifolds
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• Doubly Special Relativity with a minimum speed and the search for a quantum gravity at low energies
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• Associative realizations of the extended Snyder model
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• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity
• Snyder-de Sitter model from two-time physics
• Generalizations of Snyder model to curved spaces
• Doubly Special Relativity with a minimum speed and the Uncertainty Principle
• An explanation for the tiny value of the cosmological constant and the low vacuum energy density
• Position space versions of Magueijo-Smolin doubly special relativity proposal and the problem of total momentum
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Noncommutative Yang model and its generalizations
• Physics of Quantum Relativity through a Linear Realization
• The Stabilized Poincare-Heisenberg algebra: a Clifford algebra viewpoint
• Observables and Dynamics, Quantum to Classical, from a Relativity Symmetry and Noncommutative Geometric Perspective
• Generalized Extended Uncertainty Principles, Liouville theorem and density of states: Snyder-de Sitter and Yang models
• Quantum perturbative solutions of extended Snyder and Yang models with spontaneous symmetry breaking
• Graphene in curved Snyder space
• Review on possible gravitational anomalies
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Snyder-de Sitter meets the Grosse-Wulkenhaar model
• Relative Locality in Curved Space-time
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• On the electrodynamics of moving particles in a quasi flat spacetime with Lorentz violation and its cosmological implications
• Contracted Representation of Yang's Space-Time Algebra and Buniy-Hsu-Zee's Discrete Space-Time
• Exotic Statistics for Ordinary Particles in Quantum Gravity
• Early universe thermostatistics in curved momentum spaces
• The First Physics Picture of Contractions from a Fundamental Quantum Relativity Symmetry Including all Known Relativity Symmetries, Classical and Quantum
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• Three dimensional DKP oscillator in a curved Snyder space
• Towards new relativistic doubly $\kappa$-deformed D=4 quantum phase spaces
• Quantum Spacetime Pictures and Dynamics from a Relativity Perspective
• Electroweak symmetries from the topology of deformed spacetime with minimal length scale
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• Realizations of the Extended Snyder Model
• Extended Relativity: Beyond
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• Relativistic electrodynamics with a universal length scale
• Deformations of spacetime and internal symmetries
• Equations for fields with additional fundamental physical constants
• IR-deformed thermodynamics of quantum bouncers and the issue of dimensional reduction