A New Recursion Relation for the 6j-Symbol

Details A New Recursion Relation for the 6j-Symbol A New Recursion Relation for the 6j-Symbol

2011-03-17

arxiv.org/abs/1103.3415v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, v2: title and introduction changed, paper re-structured; Annales Henri Poincare (2011)

Scientific paper

10.1007/s00023-011-0143-y

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. Since the 6j-symbol is the basic building block of the Ponzano-Regge model for pure three-dimensional quantum gravity, we also discuss how to generalize the method to derive more general recursion relations on the full amplitudes.

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