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

TL;DR

This paper investigates the spectra of length and area operators in 2+1 Lorentzian loop quantum gravity, revealing a continuous spectrum for spacelike intervals and a discrete one for timelike intervals, aligning with spin foam results.

Contribution

It provides the first detailed analysis of length and area spectra in 2+1 Lorentzian LQG, highlighting the contrasting spectra for spacelike and timelike intervals.

Findings

Spacelike intervals have a continuous spectrum.

Timelike intervals have a discrete spectrum.

Results align with spin foam quantization.

Abstract

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.