Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity

Laurent Freidel (1) , Etera R. Livine (2, 3) , Carlo Rovelli (2, 3)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

We study the spectrum of the length and area operators in Lorentzian loop quantum gravity, in 2+1 spacetime dimensions. We find that the spectrum of spacelike intervals is continuous, whereas the spectrum of timelike intervals is discrete. This result contradicts the expectation that spacelike intervals are always discrete. On the other hand, it is consistent with the results of the spin foam quantization of the same theory.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Laurent Freidel, Etera R. Livine, Carlo Rovelli. Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity. Classical and Quantum Gravity, 2003, 20, pp.1463-1478. ⟨hal-00004792⟩