Noncommutative harmonic analysis, sampling theory and the Duflo map in 2+1 quantum gravity

DOI10.1088/0264-9381/25/4/045006zbMath1190.83070arXivhep-th/0601004OpenAlexW3100821285MaRDI QIDQ5452126

Publication date: 25 March 2008

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/0601004

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory (83C27) Geometry of quantum groups (58B32) Analogues of general relativity in lower dimensions (83C80) Methods of noncommutative geometry in general relativity (83C65) Sampling theory in information and communication theory (94A20)

Related Items (32)

Quantum gravity and Riemannian geometry on the fuzzy sphere ⋮ Closed star product on noncommutative \(\mathbb R^{3}\) and scalar field dynamics ⋮ Weak associativity and deformation quantization ⋮ Metastring theory and modular space-time ⋮ Identifying cosmological perturbations in group field theory condensates ⋮ Noncommutative \( {{\mathbb{R}}}^d \) via closed star product ⋮ Digital finite quantum Riemannian geometries ⋮ QUANTUM FIELDS ON CURVED MOMENTUM SPACE ⋮ Quantum geometric maps and their properties ⋮ Geometric Dirac operator on the fuzzy sphere ⋮ Gauge theories on quantum spaces ⋮ Almost commutative Riemannian geometry: Wave operators ⋮ Renormalization of a tensorial field theory on the homogeneous spaceSU(2)/U(1) ⋮ Involutive representations of coordinate algebras and quantum spaces ⋮ Quasi-local holographic dualities in non-perturbative 3d quantum gravity. I: Convergence of multiple approaches and examples of Ponzano-Regge statistical duals ⋮ Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett–Crane model ⋮ Toward classical geometrodynamics from the group field theory hydrodynamics ⋮ \(q\)-fuzzy spheres and quantum differentials on \(B_q[\mathrm{SU}_2\) and \(U_q(\mathrm{su}_2)\)] ⋮ Canonical quantization of non-commutative holonomies in 2 + 1 loop quantum gravity ⋮ SCALAR FIELD THEORY ON κ-MINKOWSKI SPACE–TIME AND TRANSLATION AND LORENTZ INVARIANCE ⋮ Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups ⋮ Three dimensional quantum geometry and deformed symmetry ⋮ Quantum Riemannian geometry and particle creation on the integer line ⋮ Quantum gravity on a square graph ⋮ Spin foam models and the Duflo map ⋮ ON THE ⋆-PRODUCT QUANTIZATION AND THE DUFLO MAP IN THREE DIMENSIONS ⋮ Fuzzy and discrete black hole models* ⋮ The quantum gravity disk: Discrete current algebra ⋮ Non-commutative waves for gravitational anyons ⋮ Chern-Simons theory, Stokes' theorem, and the Duflo map ⋮ New realizations of Lie algebra kappa-deformed Euclidean space ⋮ Bubbles and jackets: new scaling bounds in topological group field theories

This page was built for publication: Noncommutative harmonic analysis, sampling theory and the Duflo map in 2+1 quantum gravity