Ground state Correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions

We study density correlation functions for an impenetrable Bose gas in a finite box, with Neumann or Dirichlet boundary conditions in the ground state. We derive the Fredholm minor determinant formulas for the correlation functions. In the thermodynamic limit, we express the correlation functions in terms of solutions of non-linear differential equations which were introduced by Jimbo, Miwa, M\^ori and Sato as a generalization of the fifth Painlev\'e equations.Comment: LaTEX file, 27 pages, to appear in J. Stat. Phys. (1997

The 19-Vertex Model at critical regime ∣q∣=1|q|=1

We study the 19-vertex model associated with the quantum group $U_q(\hat{sl_2})$ at critical regime $|q|=1$. We give the realizations of the type-I vertex operators in terms of free bosons and free fermions. Using these free field realizations, we give the integral representations for the correlation functions.Comment: LaTEX2e, 19page

Form factors of the half-infinite XXZ spin chain with a triangular boundary

The half-infinite XXZ spin chain with a triangular boundary is considered in the massive regime. Two integral representations of form factors of local operators are proposed using bosonization. Sufficient conditions such that the expressions for triangular boundary conditions coincide with those for diagonal boundary conditions are identified. The expressions are compared with known results upon specializations.Using the spin-reversal property which relates the Hamiltonian with upper and lower triangular boundary conditions, new identities between multiple integrals of infinite products are extracted.Comment: LaTEX, 31 page

Free field approach to diagonalization of boundary transfer matrix : recent advances

We diagonalize infinitely many commuting operators $T_B(z)$. We call these operators $T_B(z)$ the boundary transfer matrix associated with the quantum group and the elliptic quantum group. The boundary transfer matrix is related to the solvable model with a boundary. When we diagonalize the boundary transfer matrix, we can calculate the correlation functions for the solvable model with a boundary. We review the free field approach to diagonalization of the boundary transfer matrix $T_B(z)$ associated with $U_q(A_2^{(2)})$ and $U_{q,p}(\hat{sl_N})$. We construct the free field realizations of the eigenvectors of the boundary transfer matrix $T_B(z)$. This paper includes new unpublished formula of the eigenvector for $U_q(A_2^{(2)})$. It is thought that this diagonalization method can be extended to more general quantum group $U_q(g)$ and elliptic quantum group $U_{q,p}(g)$.Comment: To appear in Group 28 : Group Theoretical Method in Physic

The SU(n) invariant massive Thirring model with boundary reflection

We study the SU(n) invariant massive Thirring model with boundary reflection. Our approach is based on the free field approach. We construct the free field realizations of the boundary state and its dual. For an application of these realizations, we present integral representations for the form factors of the local operators.Comment: LaTEX2e file, 27 page

Uq(sl^n)U_q(\hat{sl}_n)-analog of the XXZ chain with a boundary

We study $U_q(\hat{sl}_n)$ analog of the XXZ spin chain with a boundary magnetic field h. We construct explicit bosonic formulas of the vacuum vector and the dual vacuum vector with a boundary magnetic field. We derive integral formulas of the correlation functions.Comment: 24 pages, LaTEX2