Quantum Geometry on Quantum Spacetime: Distance, Area and Volume Operators

Understand

We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1].

• The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum Spacetime; this allows us to compute their spectra.
• In particular, we consider operators that can be interpreted as distances, areas, 3- and 4-volumes.
• The Minkowski distance operator between two independent events is shown to have pure Lebesgue spectrum with infinite multiplicity.