2011/12/08 by Karim Noui, Alejandro Perez, Alejandro Pérez +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical quantization #Commutative property #Computer science #Connection (principal bundle) #Cosmology and Gravitation Theories #Geometry #Hilbert space #Holonomy #Lambda #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #Regularization (linguistics) #Spin network #gr-qc
paper · pdf · doi:10.1088/1742-6596/360/1/012040
published as J.Phys.Conf.Ser. 360 (2012) 012040 · 4 pages; Proceedings of Loops'11, Madrid, to appear in Journal of Physics: Conference Series (JPCS)
arxiv created 2011/12/08 · openalex publication_date 2012/05/16 · arxiv updated 2012/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the canonical quantization of 2+1 gravity with Λ > 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 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 λ = A + λe Ae 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.