[en] We show how heavy quark effective theory (HQET), including 1/M_Q corrections, may be matched onto dynamical quark models by making a specific choice of K_μ, m and υ_μ in the p_μ = mυ_μ + K_μ expansion. We note that Wigner rotations of heavy quark spins arise at O(p²/m²) in non-relativistic models but at O(Δ_QCD/M_Q) or O(velocity - transfer) in HQET and so are necessary for a consistent treatment. (author)

[en] Identities involving 3-j and 6-j symbols are presented. They are not deducible from those already known

[en] The Askey–Wilson algebras were used to interpret the algebraic structure hidden in the Racah–Wigner coefficients of the quantum algebra $U_q({\mathfrak{sl}}_2)$. In this paper, we display an injection of a universal analog ${△}_q$ of Askey–Wilson algebras into $U_q({\mathfrak{sl}}_2)\otimes U_q({\mathfrak{sl}}_2)\otimes U_q({\mathfrak{sl}}_2)$ behind the application. Moreover we establish the decomposition rules for 3-fold tensor products of irreducible Verma $U_q({\mathfrak{sl}}_2)$-modules and of finite-dimensional irreducible $U_q({\mathfrak{sl}}_2)$-modules into the direct sums of finite-dimensional irreducible ${△}_q$-modules. As an application, we derive a formula for the Racah–Wigner coefficients of $U_q({\mathfrak{sl}}_2)$.

[en] In this paper fundamental Wigner coefficients are determined algebraically by considering the eigenvalues of certain generalized Casimir invariants. Here this method is applied in the context of both type 1 and type 2 unitary representations of the Lie superalgebra $gl(m|n)$. Extensions to the non-unitary case are investigated. A symmetry relation between two classes of Wigner coefficients is given in terms of a ratio of dimensions. (paper)

[en] On basis of various representations of the T coefficients and using limiting procedures, var//uios degenerate cases are studied for these coefficients and their relation This enables one to find relations between the hypergeometric function ₄F₃(....1) and the functions ₃F₂(...1) and ₂F₁(...1/2)

[en] The Wigner-Racah algebra of an arbitrary (finite or compact continuous) group is presented in an original way that constitutes a straightforward extension of the corresponding algebra of the rotation group. Illustrative examples are given around the rotation group and the octahedral group. The adaptation of the Wigner-Racah algebra of the double rotation group to one of its subgroups G is discussed in detail. Special emphasis is put on the case where G corresponds to the octahedral group

[en] Relation between the diagrams of sums of products of the Clebsh-Gordan coefficients and the diagrams of sums of products of the Wigner coefficients is studied. The graphic method, based on using the Clebsh-Gordan coefficients, contains phase and weight factors, which facilitate appreciably the development of the diagrams. However final diagram calculations is easier to be performed with the use of the Wigner coefficients. The last depends on the fact that proceeding from the Wigner coefficients, majority of numerical tables, algebra formulae and programs are developed for more simmetrical values. Some cases of connection between the above diagrams are studied earlier, but the problem wasn't solved finally. The arbitrary case of the open diagrams is investigated and six transmission rules are given. The data obtained are used for the momentum transformation matrixes. The rules established make it possible to come from the Clebsh-Gordan coefficient diagrams to the Wigner coefficient diagrams with minimum phases. The reverse transmission is more complicated

[en] We study successive measurements of two observables using von Neumann's measurement model. The two-pointer correlation for arbitrary coupling strength allows retrieving the initial system state. We recover Lueders rule, the Wigner formula and the Kirkwood-Dirac distribution in the appropriate limits of the coupling strength

[en] Short communication. 4 refs

[en] We revisit the superadditivity conjecture for skew information which has recently been disproved by Hansen (2007 J. Stat. Phys. 126 643). We establish two weak forms of superadditivity which are conjectured to be optimal. Our results show that in a certain sense the superadditivity is true with '50% off'