  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.
