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Non-commutative holonomies in 2+1 LQG and Kauffman's brackets

Noui, K., Perez, A., & Pranzetti, D. (2012). Non-commutative holonomies in 2+1 LQG and Kauffman's brackets. Journal of Physics: Conference Series, 360: 012040.

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1112.1825 (Preprint), 128KB
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### Creators

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Creators:
Noui, Karim, Author
Perez, Alejandro, Author
Pranzetti, Daniele1, Author
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, 67201

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Free keywords: General Relativity and Quantum Cosmology, gr-qc
Abstract: We investigate the canonical quantization of 2+1 gravity with {\Lambda} > 0 in the canonical framework of LQG. A natural regularization of the constraints of 2+1 gravity can be defined in terms of the holonomies of A\pm = A \PM \surd{\Lambda}e, where the SU(2) connection A and the triad field e are the conjugated variables of the theory. As a first step towards the quantization of these constraints we study the canonical quantization of the holonomy of the connection A_{\lambda} = A + {\lambda}e acting on spin network links of the kinematical Hilbert space of LQG. We provide an explicit construction of the quantum holonomy operator, exhibiting a close relationship between the action of the quantum holonomy at a crossing and Kauffman's q-deformed crossing identity. The crucial difference is that the result is completely described in terms of standard SU(2) spin network states.

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Dates: 2011-12-082012
Publication Status: Published in print
Pages: 4 pages; Proceedings of Loops'11, Madrid, to appear in Journal of Physics: Conference Series (JPCS)
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1112.1825
DOI: 10.1088/1742-6596/360/1/012040
URI: http://arxiv.org/abs/1112.1825
Degree: -

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Title: Loops 11: Non-Perturbative / Background Independent Quantum Gravity
Start-/End Date: 2011-05-23 - 2011-05-28

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### Source 1

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Title: Journal of Physics: Conference Series
Source Genre: Journal
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Publ. Info: Bristol : IOP Publ.
Pages: - Volume / Issue: 360 Sequence Number: 012040 Start / End Page: - Identifier: ISSN: 1742-6588
CoNE: https://pure.mpg.de/cone/journals/resource/111097776606042