Asymptotics and functional form of correlators in the XX-spin chain of finite length
We verify the functional form of the asymptotics of the spin–spin equal-time correlation function for the XX chain, predicted by the hypothesis of conformal invariance at large distances and by the bosonization procedure. We point out that the bosonization procedure also predicts the functional form of the correlators for the chains of finite length. We found the exact expression for the spin–spin equal-time correlator on a finite lattice. We find excellent agreement of the exact correlator with the prediction given by the leading asymptotics result up to very small distances. We also establish the correspondence between the value of the constant before the asymptotics for the XX chain with the expression for this constant proposed by Lukyanov and Zamolodchikov. We also evaluate the constant corresponding to the subleading term in the asymptotics in a way which is different from previous studies.

title: On the universal relations for the prefactors in correlation functions of 1D quantum liquids
abstract: For various one-dimensional quantum liquids in the framework of the Luttinger model (bosonization) we establish the relations between the coefficients before the power-law asymptotics of the correlators (prefactors) and the formfactors of the corresponding local operators. The derivation of these relations in the framework of the bosonization procedure allows to substantiate the prediction for the formfactors corresponding to the low-lying particle-hole excitations. We also obtain the formulas for the summation over the particle-hole states corresponding to the power-law asymptotics of the correlators.

title: The calculation of the leading ms corrections to the PCAC relation for the K-meson
abstract: We use the operator product expansion for the calculation of the s-quark mass correction to the K-meson PCAC relation. The leading m s correction gives a large (about 50%) contribution tothe standard PCAC relation. We obtain also the value of the SU(3) symmetry breaking parameter for the quark vacuum condensates γ =0.46.

title: EXACT GROUND STATE OF THE GENERALIZED HUBBARD MODEL FOR A WIDE RANGE OF PARAMETERS
abstract: We present the exact ground-state wave function and energy of the generalized Hubbard model, subjected to the condition that the number of doubly-occupied sites is conserved for a wide physically relevant range of parameters. For one hole and one doubly-occupied site, the existence of the ferromagnetic ground state is proved which allows one to determine the critical value of the on-site repulsion corresponding to the point of metal–insulator transition.

title: Nonrenormalization theorem in Chern-Simons theories and the fractional quantum Hall effect

title: CONSTRUCTION OF MONODROMY MATRIX IN THE F-BASIS AND SCALAR PRODUCTS IN SPIN CHAINS
abstract: We present in a simple terms the theory of the factorizing operator introduced recently by Maillet and Sanches de Santos for the spin-1/2 chains. We obtain the explicit expressions for the matrix elements of the factorizing operator in terms of the elements of the monodromy matrix. We use this results to derive the expression for the general scalar product for the quantum spin chain. We comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state. We also establish the direct correspondence between the calculations of scalar products in the F-basis and the usual basis.

title: Homeopolar excitations in a one-dimensional system of spinless fermions with nonlocal interaction