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

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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Journal of Physics: Conference Series, IOP Publishing, 2012, 360, 〈10.1088/1742-6596/360/1/012040〉
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Contributeur : Alejandro Perez <>
Soumis le : lundi 10 mars 2014 - 17:03:56
Dernière modification le : vendredi 4 janvier 2019 - 17:33:11

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K Noui, A Perez, D Pranzetti. Non-commutative holonomies in 2 + 1 LQG and Kauffman's brackets. Journal of Physics: Conference Series, IOP Publishing, 2012, 360, 〈10.1088/1742-6596/360/1/012040〉. 〈hal-00957641〉

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