Algebraic representation of correlation functions in integrable spin chains

Taking the XXZ chain as the main example, we give a review of an algebraic representation of correlation functions in integrable spin chains obtained recently. We rewrite the previous formulas in a form which works equally well for the physically interesting homogeneous chains. We discuss also the case of quantum group invariant operators and generalization to the XYZ chain.Comment: 31 pages, no figur

A recursion formula for the correlation functions of an inhomogeneous XXX model

A new recursion formula is presented for the correlation functions of the integrable spin 1/2 XXX chain with inhomogeneity. It relates the correlators involving n consecutive lattice sites to those with n-1 and n-2 sites. In a series of papers by V. Korepin and two of the present authors, it was discovered that the correlators have a certain specific structure as functions of the inhomogeneity parameters. Our formula allows for a direct proof of this structure, as well as an exact description of the rational functions which has been left undetermined in the previous works.Comment: 37 pages, 1 figure, Proof of Lemma 4.8 modifie

Form factors of descendant operators: Free field construction and reflection relations

The free field representation for form factors in the sinh-Gordon model and the sine-Gordon model in the breather sector is modified to describe the form factors of descendant operators, which are obtained from the exponential ones, \e^{\i\alpha\phi}, by means of the action of the Heisenberg algebra associated to the field $\phi(x)$. As a check of the validity of the construction we count the numbers of operators defined by the form factors at each level in each chiral sector. Another check is related to the so called reflection relations, which identify in the breather sector the descendants of the exponential fields \e^{\i\alpha\phi} and \e^{\i(2\alpha_0-\alpha)\phi} for generic values of $\alpha$. We prove the operators defined by the obtained families of form factors to satisfy such reflection relations. A generalization of the construction for form factors to the kink sector is also proposed.Comment: 29 pages; v2: minor corrections, some references added; v3: minor corrections; v4,v5: misprints corrected; v6: minor mistake correcte

Raising and lowering operators, factorization and differential/difference operators of hypergeometric type

Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight. Using the Infeld-Hull factorization method, we generate from the raising and lowering operators the second order self-adjoint differential/difference operator of hypergeometric type.Comment: LaTeX, 24 pages, iopart style (late submission

Raising and lowering operators and their factorization for generalized orthogonal polynomials of hypergeometric type on homogeneous and non-homogeneous lattice

We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal polynomials, namely, those difference of orthogonal polynomials that satisfy a similar difference equation of hypergeometric type.Comment: LaTeX, 19 pages, (late submission to arXiv.org

Bimaximal Neutrino Mixing with Discrete Flavour Symmetries

In view of the fact that the data on neutrino mixing are still compatible with a situation where Bimaximal mixing is valid in first approximation and it is then corrected by terms of order of the Cabibbo angle, we present examples where these properties are naturally realized. The models are supersymmetric in 4-dimensions and based on the discrete non-Abelian flavour symmetry S4.Comment: 8 pages, 1 figure; contribution prepared for DISCRETE'10 - Symposium on Prospects in the Physics of Discrete Symmetrie

Exact evaluation of density matrix elements for the Heisenberg chain

We have obtained all the density matrix elements on six lattice sites for the spin-1/2 Heisenberg chain via the algebraic method based on the quantum Knizhnik-Zamolodchikov equations. Several interesting correlation functions, such as chiral correlation functions, dimer-dimer correlation functions, etc... have been analytically evaluated. Furthermore we have calculated all the eigenvalues of the density matrix and analyze the eigenvalue-distribution. As a result the exact von Neumann entropy for the reduced density matrix on six lattice sites has been obtained.Comment: 33 pages, 4 eps figures, 3 author

Neutrino masses and mixing

Status of determination of the neutrino masses and mixing is formulated and possible uncertainties, especially due to presence of the sterile neutrinos, are discussed. The data hint an existence of special ``neutrino'' symmetries. If not accidental these symmetries have profound implications and can substantially change the unification program. The key issue on the way to underlying physics is relations between quarks and leptons. The approximate quark-lepton symmetry or universality can be reconciled with strongly different patterns of masses and mixings due to nearly singular character of the mass matrices or screening of the Dirac structures in the double see-saw mechanism.Comment: 11 pages, latex, iopams.sty, 3 figures. Invited talk given at TAUP2005, September 10 - 14, 2005, Zaragoza, Spai

Hyperspherical harmonics with arbitrary arguments

The derivation scheme for hyperspherical harmonics (HSH) with arbitrary arguments is proposed. It is demonstrated that HSH can be presented as the product of HSH corresponding to spaces with lower dimensionality multiplied by the orthogonal (Jacobi or Gegenbauer) polynomial. The relation of HSH to quantum few-body problems is discussed. The explicit expressions for orthonormal HSH in spaces with dimensions from 2 to 6 are given. The important particular cases of four- and six-dimensional spaces are analyzed in detail and explicit expressions for HSH are given for several choices of hyperangles. In the six-dimensional space, HSH representing the kinetic energy operator corresponding to i) the three-body problem in physical space and ii) four-body planar problem are derived.Comment: 18 pages, 1 figur