  Connes' formula defines a distance in loop quantum gravity, via the spinfoam
Dirac operator. A simple notion of spectral distance on a graph can be extended
do the discrete Lorentzian context, providing a physically natural example of
Lorentzian spectral geometry, with a neat space of Dirac operators. The Hilbert
structure of the fermion space is Lorentz covariant rather than invariant.
