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arXiv · 1306.3246

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

Jibril Ben Achour·Marc Geiller·Karim Noui·Chao Yu
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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 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.

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Jibril Ben Achour, Marc Geiller, Karim Noui, Chao Yu. 2013-06-13. Spectra of geometric operators in three-dimensional LQG: From discrete to continuous. https://doi.org/10.1103/physrevd.89.064064

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