Canonical quantization of non-commutative holonomies in 2 + 1 loop quantum gravity

DOI10.1007/JHEP10(2011)036zbMath1303.83013arXiv1105.0439WikidataQ64007760 ScholiaQ64007760MaRDI QIDQ489627

Karim Noui, Daniele Pranzetti, Alejandro Perez

Publication date: 20 January 2015

Published in: Journal of High Energy Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.0439

zbMATH Keywords

topological field theoriesquantum groupsmodels of quantum gravity

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Quantization in field theory; cohomological methods (81T70) Quantization of the gravitational field (83C45) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Topological field theories in quantum mechanics (81T45) Constrained dynamics, Dirac's theory of constraints (70H45) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Pencils, nets, webs in algebraic geometry (14C21)

Related Items (12)

Statistical entropy of a BTZ black hole from loop quantum gravity ⋮ Extensions of the Duflo map and Chern-Simons expectation values ⋮ Quantum gravity kinematics from extended TQFTs ⋮ Quasi-local holographic dualities in non-perturbative 3d quantum gravity. I: Convergence of multiple approaches and examples of Ponzano-Regge statistical duals ⋮ Quasi-local holographic dualities in non-perturbative 3d quantum gravity. II: From coherent quantum boundaries to \(BMS_{3}\) characters ⋮ On the Weyl tensor classification in all dimensions and its relation with integrability properties ⋮ Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups ⋮ q-deformed 3D loop gravity on the torus ⋮ 3d quantum gravity: coarse-graining and \(q\)-deformation ⋮ Deformed spinor networks for loop gravity: towards hyperbolic twisted geometries ⋮ Encoding curved tetrahedra in face holonomies: phase space of shapes from group-valued moment maps ⋮ The spin-foam approach to quantum gravity

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