Related papers: Spin Multiplicities
The single pion production (SPP) in the charged-current neutrino (antineutrino) scattering off the polarized nucleon is discussed. The spin asymmetry is predicted within two approaches. The spin polarizations of the target nucleon that are…
We study the Kronecker symbol $\left(\frac st\right)$ for the sequence of the convergents $s/t$ of a purely periodic continued fraction expansion. Whereas the corresponding sequence of Jacobi symbols is always periodic, it turns out that…
We give a new expression for the expected number of inversions in the product of n random adjacent transpositions in the symmetric group S_{m+1}. We then derive from this expression the asymptotic behaviour of this number when n scales with…
Double spin asymmetries in the diffractive $Q \bar Q$ and $J/\Psi$ leptoproduction are discussed. It is shown that the asymmetries for longitudinally polarized lepton and longitudinally or transversely polarized proton can be used to study…
Proton is a composite particle, so its spin S_P is made from the spins of the partons which the proton consists of. The discrepancy between S_P = 1/2 and the experimentally detected sum of the parton spins was named Proton Spin Puzzle.…
For a positive integer $n$, let $p(n)$ be the number of ways to express $n$ as a sum of positive integers. In this note, we revisit the derivation of the Rademacher's convergent series for $p(n)$ in a pedagogical way, with all the details…
The problem of decomposing the Kronecker product of $S_n$ characters is one of the last major open problems in the ordinary representation theory of the symmetric group $S_n$. Here we prove upper and lower polynomial bounds for the…
An expression for the oscillatory part of an asymptotic formula for the relativistic spin network amplitude for a 4-simplex is given. The amplitude depends on specified areas for each two-dimensional face in the 4-simplex. The asymptotic…
Answering a question of Geoff Robinson, we compute the large n limiting proportion of i(n,q)/q^[n^2/2], where i(n,q) denotes the number of involutions in GL(n,q). We give similar results for the finite unitary, symplectic, and orthogonal…
We investigate certain classes of integrable classical or quantum spin systems. The first class is characterized by the recursively defined property $P$ saying that the spin system consists of a single spin or can be decomposed into two…
Projective irreps of (Z_N)^2 can be labelled by divisors n of N. A product of two irreps, labelled by n and n', can be decomposed into projective irreps labelled by M, where M strongly depends on the arithmetic structure of N, n, n' and…
Accounting for double-logarithms of x and running QCD coupling leads to expressions for both the non-singlet and singlet components of $g_1$. These expressions manifest the Regge asymptotics when x ->0 and differ considerably from the DGLAP…
A representation for the Riemann zeta function valid for arbitrary complex $s=\sigma+it$ is $\zeta(s)=\sum_{n=0}^\infty A(n,s)$, where \[A(n,s)=\frac{2^{-n-1}}{1-2^{1-s}} \sum_{k=0}^n \left(\!\begin{array}{c}n\\k\end{array}\!\right)…
We use representation theory of $S_n$ to analyze the mixing of permutation cycle type statistics $a_j(\sigma) = ${# of $j$-cycles of $\sigma$} for any fixed $j$ and $\sigma$ resulting from a random $i$-cycle walk on $S_n$. We also derive…
Let J and J* be subsets of Z+ such that 0,1\in J and 0\in J*. For infinitely many n, let k=(k_1,..., k_n) be a vector of nonnegative integers whose sum M is even. We find an asymptotic expression for the number of multigraphs on the vertex…
A systematic presentation of spinors in various dimensions is given.
We discuss permutation representations which are obtained by the natural action of $S_n \times S_n$ on some special sets of invertible matrices, defined by simple combinatorial attributes. We decompose these representations into…
The invertable map of spin state density operator onto quasiprobability distribution of three continuous variables is constructed. The connection with two-mode electromagnetic field oscillators is discussed. The inversion formula for…
The aim of this work is to prove that it is possible to realise an optical system which produces as output a light intensity that can be expressed in the same mathematical form of the spin glass Hamiltonian. The optical system under study…
Consider a spin s prepared in a pure state. It is shown that, generically, the moduli of the (2s+1) spin components along three directions in space determine the state unambiguously. These probabilities are accessible experimentally by…