Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semiclassical Analysis of the Wigner $12j$ Symbol with One Small Angular
  Momentum   We derive an asymptotic formula for the Wigner $12j$ symbol, in the limit of
one small and 11 large angular momenta. There are two kinds of asymptotic
formulas for the $12j$ symbol with one small angular momentum. We present the
first kind of formula in this paper. Our derivation relies on the techniques
developed in the semiclassical analysis of the Wigner $9j$ symbol [L. Yu and R.
G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant
form of the multicomponent WKB wave-functions to derive asymptotic formulas for
the $9j$ symbol with small and large angular momenta. When applying the same
technique to the $12j$ symbol in this paper, we find that the spinor is
diagonalized in the direction of an intermediate angular momentum. In addition,
we find that the geometry of the derived asymptotic formula for the $12j$
symbol is expressed in terms of the vector diagram for a $9j$ symbol. This
illustrates a general geometric connection between asymptotic limits of the
various $3nj$ symbols. This work contributes the first known asymptotic formula
for the $12j$ symbol to the quantum theory of angular momentum, and serves as a
basis for finding asymptotic formulas for the Wigner $15j$ symbol with two
small angular momenta.

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The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat