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- W2051037913 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 Apm = 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." @default.
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- W2051037913 date "2012-05-16" @default.
- W2051037913 modified "2023-10-15" @default.
- W2051037913 title "Non-commutative holonomies in 2 + 1 LQG and Kauffman's brackets" @default.
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- W2051037913 doi "https://doi.org/10.1088/1742-6596/360/1/012040" @default.
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