Related papers: Asymptotes in SU(2) Recoupling Theory: Wigner Matr…
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…
A new uniform asymptotic approximation for the Wigner $6j$ symbol is given in terms of Wigner rotation matrices ($d$-matrices). The approximation is uniform in the sense that it applies for all values of the quantum numbers, even those near…
We revisit the the large spin asymptotics of 15j symbols in terms of cosines of the 4d Euclidean Regge action, as derived by Barrett and collaborators using a saddle point approximation. We bring it closer to the perspective of area-angle…
We prove an asymptotic formula for the number of $n$-dimensional representations of the group $\mathrm{SU}(3)$. Main tools for the proof are Wright's Circle Method and the Saddle Point Method.
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 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…
We present the first complete derivation of the well-known asymptotic expansion of the SU(2) 6j symbol using a coherent state approach, in particular we succeed in computing the determinant of the Hessian matrix. To do so, we smear the…
We prove that the asymptotic behavior of the recoupling coefficients of the symmetric group is characterized by a quantum marginal problem -- namely, by the existence of quantum states of three particles with given eigenvalues for their…
Within the framework of the theory of irreducible tensor operators, using well-known general analytical results for double sums ($\sum_{jm}$) of products of two $3j$-Wigner symbols, analytical expressions for single sums ($\sum_m$) for the…
A general procedure for the derivation of SU(3)\supset U(2) reduced Wigner coefficients for the coupling (\lambda_{1}\mu_{1})\times (\lambda_{2}\mu_{2})\downarrow (\lambda\mu)^{\eta}, where \eta is the outer multiplicity label needed in the…
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…
Based on the multivariate saddle point method we study the asymptotic behavior of the characteristic polynomials associated to Wishart type random matrices that are formed as products consisting of independent standard complex Gaussian and…
Using a generating function for the Wigner's $D$-matrix elements of $SU(3)$ Weyl's character formula for $SU(3)$ is derived using Schwinger's technique.
We derive the leading asymptotic limit of the Wigner $3j$-symbol from a stationary phase approximation of a twelve dimensional integral, obtained from an inner product between two exact Bargmann wavefunctions. We show that, by the…
Recoupling coefficients (3nj symbols) are unitary transformations between binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum operators. They have been used in a variety of applications in spectroscopy, quantum…
We consider integrals on unitary groups $U_d$ of the form $$\int_{U_d}U_{i_1j_1}... U_{i_qj_q}U^*_{j'_{1}i'_{1}} ... U^*_{j'_{q'}i'_{q'}}dU$$ We give an explicit formula in terms of characters of symmetric groups and Schur functions, which…
We establish asymptotic formulae for general joint moments of characteristic polynomials and their higher-order derivatives associated with matrices drawn randomly from the groups $\mathrm{USp}(2N)$ and $\mathrm{SO}(2N)$ in the limit as…
We study the Dirichlet-to-Neumann map for the stationary linear equation of elasticity in a bounded domain in R d , d $\ge$ 2, with smooth boundary. We show that it can be approximated by a pseudodifferential operator on the boundary with a…
We present the asymptotic formula for the Wigner 9j-symbol, valid when all quantum numbers are large, in the classically allowed region. As in the Ponzano-Regge formula for the 6j-symbol, the action is expressed in terms of lengths of edges…