1306.3246 (Jibril Ben Achour et al.)

Spectra of geometric operators in three-dimensional LQG: From discrete
to continuous    [PDF]

Jibril Ben Achour, Marc Geiller, Karim Noui, Chao Yu

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 SU(2) Ashtekar-Barbero framework, the spectra are discrete and depend on the Barbero-Immirzi parameter $\gamma$ 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 $\gamma$-independent.

View original: http://arxiv.org/abs/1306.3246