We shall review the DFR approach to the to the quantisation of spacetime: motivations, heuristics, uncertainty relations, interpretation.
In the basic DFR model, the background metric is fixed to flat Minkowski (thus no attempt is made to dynamically couple it with gravity), and the localisation algebra is generated by non commuting selfadjoint operators whose uncertainty relations are interpreted as a stability condition of spacetime under localisation alone. The idealised, hypothetical range of validity of the model encompasses very few processes of very high energy. It provides an arena where to focus some technical and conceptual difficulties.
If time permits, some aspects of the effective nonlocal quantum field on classical spacetime will be discussed, where nonlocality stems out of the noncommutativyity of the localisation algebra. Criticalities and open problems will be sketched.
The discussion will possibly prosecute in a subsequent seminar, where some aspects of the quantum geometry of the model also will be presented, as well as some outlook.
KEYWORDS: spacetime quantisation, operator algebra, operator theory, quantum gravity, nonlocal quantum field theory.