17 feb 2016 -- 15:00
Aula Dal Passo, Dip.Matematica, Università "Tor Vergata", Roma
Abstract.
The features of Quantum Mechanics which were new for Classical Physics, and still are definitely counter - intuitive, can all be summarized in a statement: the $C^*$ Algebra generated by all observables is non-commutative. In Quantum Field Theory, neglecting gravitational forces between elementary particles, observables measured in spacelike separate regions commute, which makes the overall $C^*$ algebra 'more non-commutative'. But spacetime regions are subset of Minkowski space (or of a curved Einstein manifold), a classical space. But if we do not neglect gravity among the interactions between elementary particles, spacetime cannot be described by a classical manifold in the small. It becomes a Quantum Space. We will review a simple model of Quantum Spacetime, the spectral properties of some of its geometric operators, the problem of interacting quantum fields on quantum spacetime, and close with few words on the cosmological consequences of the model.