Recurrence relation for the 6j-symbol of suq(2) as a symmetric eigenvalue problem

DOI10.1142/S0219887815501170zbMath1354.81028arXiv1009.2261MaRDI QIDQ3455925

Igor Khavkine

Publication date: 11 December 2015

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.2261

zbMATH Keywords

quantum groupeigenvalue problemrecurrence relation\(6j\)-symbol

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Quantization of the gravitational field (83C45) Groups and algebras in quantum theory and relations with integrable systems (81R12) Applications of group representations to physics and other areas of science (20C35) Numerical aspects of recurrence relations (65Q30)

Uses Software

• LAPACK

Cites Work

• \(6j\) symbols for \(u_q(\mathfrak{sl}_2)\) and non-Euclidean tetrahedra
• Quantum field theory and the Jones polynomial
• State sum invariants of 3-manifolds and quantum \(6j\)-symbols
• 3-valent graphs and the Kauffman bracket
• Quantum deformation of two four-dimensional spin foam models
• q -deformed spin foam models of quantum gravity
• A Set of Orthogonal Polynomials That Generalize the Racah Coefficients or $6 - j$ Symbols
• General recurrence relations for Clebsch-Gordan coefficients of the quantum algebra U_q(su₂)
• Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)
• Three-dimensional gravity from the Turaev-Viro invariant
• Linking topological quantum field theory and nonperturbative quantum gravity
• The geometry of quantum spin networks

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