Kinematics of a relativistic particle with de Sitter momentum space

Abstract

We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and equations of motion for such free particle. We study the action of deformed relativistic symmetries on the phase space and derive explicit formulas for the action of the deformed Poincare' group. Finally we provide a discussion on parametrization of the particle worldlines stressing analogies and differences with ordinary relativistic kinematics.

arXiv commentRevTeX, 12 pages, no figures

References in corpus (23)

• 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
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• Deformed Boost Transformations That Saturate at the Planck Scale
• Observer-independent quanta of mass and length
• Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
• Deformed Special Relativity and Deformed Symmetries in a Canonical Framework
• Fock space, quantum fields and kappa-Poincaré symmetries
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• Bounds on an energy-dependent and observer-independent speed of light from violations of locality
• Quantum group symmetry and particle scattering in (2+1)-dimensional quantum gravity
• The Free Particle in Deformed Special Relativity
• Topological field theory and the quantum double of SU(2)
• Velocity of particles in Doubly Special Relativity
• Large-scale non-locality in "doubly special relativity" with an energy-dependent speed of light
• Lorentz invariant field theory on kappa-Minkowski space
• Anatomy of a deformed symmetry: field quantization on curved momentum space
• Rainbow statistics
• Quantum fields, non-locality and quantum group symmetries
• Particles as Wilson lines of gravitational field
• Hidden entanglement at the Planck scale: loss of unitarity and the information paradox

Cited by in corpus (16)

• Minimal Length Scale Scenarios for Quantum Gravity
• Quantum Spacetime Phenomenology
• The principle of relative locality
• On the fate of Lorentz symmetry in relative-locality momentum spaces
• Modeling transverse relative locality
• Dual redshift on Planck-scale-curved momentum spaces
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
• Deformed Carroll particle from 2+1 gravity
• Multi-particle systems in $\kappa$-Poincaré inspired by 2+1D gravity
• Deformed phase spaces with group valued momenta
• Localization and diffusion in polymer quantum field theory
• Longitudinal and transverse relativity of spacetime locality in Planck-scale-deformed phase spaces
• Non-local quantum field theory from doubly special relativity
• $\kappa$-Poincaré phase space: speed of massless particles and relativity of spacetime locality
• Parity at the Planck scale