Urs and Mitchel aren't fans of polymer quantization used in LQG to quantize Ashketer variables, they regard it as unphysical and unconnected to the rest of physics.(adsbygoogle = window.adsbygoogle || []).push({});

LQG based on "polymer quantization" and "generalized connection" is a dead end.

fair enough.

is there a procedure to nonperturbative quantization of Ashketer variables that is physical or is more promising than polymer quantization.

how could an LQG theorist quantize Ashketar variables that could be a serious candidate for QG.

Since I read Urs and Mitchell's concerns in two threads, I did research on other ways to quantize Ashketer variables.

I have in mind the paper below avoid the concerns Urs and Mitchell have about polymer quantization of ahsketer variables, by offering a more realistic quantization?

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-introduced flux formulation of 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 the full 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.

Comments: 72 pages, 6 figures

Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)

Cite as: arXiv:1506.08571 [gr-qc]

(or arXiv:1506.08571v1 [gr-qc] for this version)

Submission history

From: Marc Geiller [view email]

[v1]Mon, 29 Jun 2015 10:25:11 GMT (1370kb,D)

some of the results of polymer quantization of Ashketer variables carries over.

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# I Other procedures to quantize Ashketer variables

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