Abstract
We study and compare the spectra of geometric operators (length and area) in the quantum kinematics of two formulations of three-dimensional Lorentzian loop quantum gravity. In the Ashtekar-Barbero framework, the spectra are discrete and depend on the Barbero-Immirzi parameter exactly like in the four-dimensional case. However, we show that when working with the self-dual variables and imposing the reality conditions the spectra become continuous and independent.
- Received 2 July 2013
DOI:https://doi.org/10.1103/PhysRevD.89.064064
© 2014 American Physical Society