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Asymptotic Limits of the Wigner -Symbol with Small Quantum Numbers
We present new asymptotic formulas for the Wigner -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 -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 -symbol with two,
three, and four small quantum numbers are based on the geometric figures of the
-, -, and -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.Comment: 13 pages, 8 figure
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