Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity

Carlo Rovelli (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - E4 Gravité quantique

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.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique mathématique [math-ph]

Carlo Rovelli. Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity. 2014. ⟨hal-01476566⟩