Speaker
Gherardo Piacitelli
Description
We will review the DFR approach to Quantum Space-
Time and discuss the
state of the art and the open issues.
The DFR model is a fully covariant model of flat quantum
spacetime
generated by selfadjoint coordinates, where covariance
is unitarily
implemented, and the commutation relations among the
coordinates are
derived from a stability condition of spacetime under
localisation
alone. It must be regarded as a sort of analogue of
semiclassical
quantisation, providing the noncommutative geometric
background for the
quantum theory of fields at an intermediate regime,
where few processes
take place at very high energy; attempts to construct
dynamical models
also will be shortly reviewed and discussed.
The stability condition is enforced through uncertainty
relations which
should prevent the purely kynematical black-hole
formation. The quantum
geometry arising from the interplay of the universal
differential
calculus with the specific algebra of the model provides a
precise
framework for discussing bounds to measurements of
position,length, and
n-volumes operators.
We will conclude with an outlook.
References: [arXiv:hep-th/0303037], [arXiv:1005.2130],
[arXiv:hep-th/0301100],[arXiv:1201.2519],
[arXiv:1206.3067].
See also the review [arXiv:1004.5261v3].
