Snyder-type spaces, twisted Poincar\'e algebra and addition of momenta

Understand

We discuss a generalisation of the Snyder model that includes all the possible deformations of the Heisenberg algebra compatible with Lorentz invariance, in terms of realisations of the noncommutative geometry.

• The corresponding deformed addition of momenta, the twist and the $R$-matrix are calculated to first order in the deformation parameters for all models.
• In the particular case of the Snyder realisation, the exact formula for the twist is obtained.