Unambiguous quantum gravity phenomenology respecting lorentz symmetry

We describe a refined version of a previous proposal for the exploration of quantum gravity phenomenology. Unlike the original scheme, the one presented here is free from sign ambiguities while it shares with the previous one the essential features. It focuses on effects that could be thought as arising from a fundamental granularity of quantum space-time. The sorts of schemes we consider are in sharp contrast with the simplest scenarios in that such granularity is assumed to respect Lorentz invariance but it remains otherwise unspecified. The proposal is fully observer covariant, it involves nontrivial couplings of curvature to matter fields and leads to a well defined phenomenology. We present the effective Hamiltonian which could be used to analyze concrete experimental situations, and we shortly review the degree to which this proposal is in line with the fundamental ideas behind the equivalence principle.