Snyder Momentum Space in Relative Locality
arXiv:1308.0300 · doi:10.1103/PhysRevD.90.076010
Abstract
The standard approaches of phenomenology of Quantum Gravity have usually explicitly violated Lorentz invariance, either in the dispersion relation or in the addition rule for momenta. We investigate whether it is possible in 3+1 dimensions to have a non local deformation that preserves fully Lorentz invariance, as it is the case in 2+1D Quantum Gravity. We answer positively to this question and show for the first time how to construct a homogeneously curved momentum space preserving the full action of the Lorentz group in dimension 4 and higher, despite relaxing locality. We study the property of this relative locality deformation and show that this space leads to a noncommutativity related to Snyder spacetime.
22 pages, 6 figures, matches version accepted in PRD
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- Relativistic deformed kinematics from momentum space geometry
- A (2+1) non-commutative Drinfel'd double spacetime with cosmological constant
- Geometric interpretation of Planck-scale-deformed co-products
- Planck-scale-deformed relativistic symmetries and diffeomorphisms in momentum space
- Relative-locality effects in Snyder spacetime
- Towards (3+1) gravity through Drinfel'd doubles with cosmological constant
- Relativistic deformed kinematics: from flat to curved spacetimes
- Space-time thermodynamics in momentum dependent geometries
- Mixing coproducts for theories with particle-dependent relativistic properties
- Relative-locality geometry for the Snyder model
- Twisting loops and global momentum non-conservation in Relative Locality
- Anti-de Sitter Momentum Space in 3D and 4D Quantum Gravity