相关论文: On summation of $3j$-Wigner symbols
We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's…
The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in…
We present new sum rules for $3jm$ coefficients, which involve, in addition to the usual weighting factor $(2j + 1)$ where $j$ is an angular momentum, the quantity $[j(j + 1)]^k$ with $k \ge 1$. The sum rules appear for instance in the…
We present an efficient implementation for the evaluation of Wigner 3j, 6j, and 9j symbols. These represent numerical transformation coefficients that are used in the quantum theory of angular momentum. They can be expressed as sums and…
The contribution of Jacques Raynal to angular-momentum theory is highly valuable. In the present article, I intend to recall the main aspects of his work related to Wigner $3j$ symbols. It is well known that the latter can be expressed with…
The 3-regular graphs representing sums over products of Wigner 3-jm symbols are drawn on up to 12 vertices (complete to 18j-symbols), and the irreducible graphs on up to 14 vertices (complete to 21j-symbols). The Lederer-Coxeter-Frucht…
We derive a new asymptotic formula for the Wigner $9j$-symbol, in the limit of one small and eight large angular momenta, using a novel gauge-invariant factorization for the asymptotic solution of a set of coupled wave equations. Our…
Yu and Littlejohn recently studied in arXiv:1104.1499 some asymptotics of Wigner symbols with some small and large angular momenta. They found that in this regime the essential information is captured by the geometry of a tetrahedron, and…
We show that general $3n-j (n>2)$ symbols of the first kind and the second kind for the group SU(2) can be reformulated in terms of binomial coefficients. The proof is based on the graphical technique established by Yutsis, et al. and…
We study a class of SU(N) Wigner 6j symbols involving two fundamental representations, and derive explicit formulae for all 6j symbols in this class. Our formulae express the 6j symbols in terms of the dimensions of the involved…
In this paper we employ a novel technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index $J$) of generic Wigner matrix elements…
The coupling coefficients (3j-symbols) for the symmetric (most degenerate) irreducible representations of the orthogonal groups SO(n) in a canonical basis and different semicanonical (tree) bases [with SO(n) restricted to SO(n')\times…
For each generic $(3\mbox{-}j)$ the column parities, $2(j \pm m)$, define $3$ intrinsic parities: $\alpha, \beta,\gamma$. In algebra $so(3)$ only $(3\mbox{-}j)\_{\alpha}$ exists whereas super-algebra $osp(1|2)$ admits $3$ kinds of…
The use of orthogonal polynomials for integral models on the lattice is applied to the 3nj-symbols that appear in the coupling of several angular momenta. These symbols are connected to the Ponzano-Regge method to solve the Einstein…
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…
The generating function method that we had developing has various applications in physics and not only interress undergraduate students but also physicists. We solve simply difficult problems or unsolved commonly used in quantum, nuclear…
Total-angular-momentum (TAM) waves provide a set of basis functions for scalar, vector, and tensor fields that can be used in place of plane waves and that reflect the rotational symmetry of the spherical sky. Here we discuss three-point…
Ten values of 12-j symbols of the first kind published earlier are challenged by values calculated with an independent Python program. The program first implements a narrow class of square roots of rational numbers, utilizing Python's…
Modular double of quantum group SL_q(2,R) with |q|=1 has a series of selfadjoint irreducible representations parameterized by s. Ponsot and Teschner considered a decomposition of the tensor product of two representations into irreducibles.…
In the paper a simple explicit formula for an arbitrary $3j$-symbol for the Lie algebra $\mathfrak{gl}_3$ is given. More precise necessary conditions for non-vanishing of a $3j$-symbol are given, in the case when these conditions hold we…