# Spectra of length and area in (2 + 1) Lorentzian loop quantum gravity

@article{Freidel2003SpectraOL,
title={Spectra of length and area in (2 + 1) Lorentzian loop quantum gravity},
author={Laurent Freidel and Etera R. Livine and Carlo Rovelli},
journal={Classical and Quantum Gravity},
year={2003},
volume={20},
pages={1463-1478}
}
• Published 18 December 2002
• Physics
• Classical and Quantum Gravity
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.
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