I think this will probably turn out to be one of the most important QG papers this quarter. It is based on some very interesting and groundbreaking work by Dittrich and Geiller that has come out over the past year and a half. I'll give links to that after posting the main abstract:(adsbygoogle = window.adsbygoogle || []).push({});

http://arxiv.org/abs/1506.08571

A new realization of quantum geometry

Benjamin Bahr, Bianca Dittrich, Marc Geiller

(Submitted on 29 Jun 2015)

We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introducedflux formulationof loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states are built upon it by creating local curvature excitations. The inner product induces a discrete topology on the gauge group, which turns out to be an essential ingredient for the construction of a continuum limit Hilbert space. This leads to a representation of thefull holonomy-flux algebra of loop quantum gravity which is unitarily-inequivalent to the one based on the Ashtekar-Isham-Lewandowski vacuum.It therefore provides a new notion of quantum geometry. We discuss how the spectra of geometric operators, including holonomy and area operators, are affected by this new quantization. In particular, we find that the area operator is bounded, and that there are two different ways in which the Barbero-Immirzi parameter can be taken into account. The methods introduced in this work open up new possibilities for investigating further realizations of quantum geometry based on different vacua.

72 pages, 6 figures

Here are a couple of papers they build on:

B. Dittrich and M. Geiller, “A new vacuum for loop quantum gravity”,

Class. Quant. Grav. (2014) http://arxiv.org/abs/1401.6441 .

B. Dittrich and M. Geiller, “Flux formulationof loop quantum gravity: Classical framework”,

Class. Quant. Grav. (2015), http://arxiv.org/abs/1412.3752 .

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# A new realization of quantum geometry

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