2011

A New Recursion Relation for the 6j-Symbol

Bonzom, Valentin, Livine, Etera R.

Understand

The 6j-symbol is a fundamental object from the re-coupling theory of SU(2) representations.

In the limit of large angular momenta, its asymptotics is known to be described by the geometry of a tetrahedron with quantized lengths.
This article presents a new recursion formula for the square of the 6j-symbol.
In the asymptotic regime, the new recursion is shown to characterize the closure of the relevant tetrahedron.

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Similar

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2003
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M. Carfora, A. Marzuoli and M. Rasetti, “Quantum Tetrahedra,” J. Phys. Chem. A 113
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2009
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M. Dupuis and E.R Livine, “Pushing Further the Asymptotics of the 6j-symbol,” Phys.Rev.D80 (2009) 024035 [arXiv:0905.4188]
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V. Aquilanti, H. M. Haggard, A. Hedeman, N. Jeevanjee, R. G. Littlejohn and L. Yu, “Semiclassical Mechanics of the Wigner 6 j 6j -Symbol,” arXiv:1009.2811 [math-ph]
Original
Cited in the paper.
V. Bonzom and P. Fleury, “Asymptotics of Wigner 3nj-symbols with Small and Large Angular Momenta: an Elementary Method,” arXiv:1108.1569 [quant-ph]
Original
Cited in the paper.

Then

J.W. Barrett and I. Naish-Guzman, “The Ponzano-Regge model,” Class.Quant.Grav.26 (2009) 155014 [arXiv:0803.3319]
Original
2009
Later among the works it cites.
M. Dupuis and E. R. Livine, “The 6j-symbol: Recursion, Correlations and Asymptotics,” Class. Quant. Grav. 27
Original
2010
Later among the works it cites.
J. W. Barrett, W. J. Fairbairn and F. Hellmann, “Quantum gravity asymptotics from the SU(2) 15j symbol,” Int. J. Mod. Phys. A25
Original
2010
Later among the works it cites.
V. Bonzom, E. R. Livine and S. Speziale, “Recurrence relations for spin foam vertices,” Class. Quant. Grav. 27
Original
2010
Later among the works it cites.
R. G. Littlejohn and L. Yu, “Semiclassical Analysis of the Wigner 9 J 9J -Symbol with Small and Large Angular Momenta,” Phys. Rev. A 83
Original
2011
Closest in time.
V. Bonzom, “Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex,” Phys. Rev. D 84
Original
2011
Closest in time.
A. Baratin and L. Freidel, “Hidden Quantum Gravity in 3d Feynman diagrams,” Class.Quant.Grav.24 (2007) 1993-2026 [arXiv:gr-qc/0604016]
2026
Closest in time.
R. J. Dowdall, H. Gomes and F. Hellmann, “Asymptotic analysis of the Ponzano-Regge model for handlebodies,” J. Phys. A 43
Original
2027
Closest in time.
L. Freidel and E.R. Livine, “Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory,” Class.Quant.Grav.23 (2006) 2021-2062 [arXiv:hep-th/0502106]
2062
Closest in time.

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