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arXiv · 1104.3641

Asymptotic Limits of the Wigner $15J$-Symbol with Small Quantum Numbers

Liang Yu
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Abstract

We present new asymptotic formulas for the Wigner $15j$-symbol with two, three, or four small quantum numbers, and provide numerical evidence of their validity. These formulas are of the WKB form and are of a similar nature as the Ponzano-Regge formula for the Wigner $6j$-symbol. They are expressed in terms of edge lengths and angles of geometrical figures associated with angular momentum vectors. In particular, the formulas for the $15j$-symbol with two, three, and four small quantum numbers are based on the geometric figures of the $9j$-, $6j$-, and $3j$-symbols, respectively, The geometric nature of these new asymptotic formulas pave the way for further analysis of the semiclassical limits of vertex amplitudes in loop quantum gravity models.

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Liang Yu. 2011-04-19. Asymptotic Limits of the Wigner $15J$-Symbol with Small Quantum Numbers. https://arxiv.org/abs/1104.3641

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