Vertex Operators and Matrix Elements of Uq(su(2)k)U_q(su(2)_k) via Bosonization

We construct bosonized vertex operators (VOs) and conjugate vertex operators (CVOs) of $U_q(su(2)_k)$ for arbitrary level $k$ and representation $j\leq k/2$. Both are obtained directly as two solutions of the defining condition of vertex operators - namely that they intertwine $U_q(su(2)_k)$ modules. We construct the screening charge and present a formula for the n-point function. Specializing to $j=1/2$ we construct all VOs and CVOs explicitly. The existence of the CVO allows us to place the calculation of the two-point function on the same footing as $k=1$; that is, it is obtained without screening currents and involves only a single integral from the CVO. This integral is evaluated and the resulting function is shown to obey the q-KZ equation and to reduce simply to both the expected $k=1$ and $q=1$ limits.Comment: 20 pages, LaTex. Minor change

The Dynamical Correlation Function of the XXZ Model

We perform a spectral decomposition of the dynamical correlation function of the spin $1/2$ XXZ model into an infinite sum of products of form factors. Beneath the four-particle threshold in momentum space the only non-zero contributions to this sum are the two-particle term and the trivial vacuum term. We calculate the two-particle term by making use of the integral expressions for form factors provided recently by the Kyoto school. We evaluate the necessary integrals by expanding to twelfth order in $q$. We show plots of $S(w,k)$, for $k=0$ and $\pi$ at various values of the anisotropy parameter, and for fixed anisotropy at various $k$ around $0$ and $\pi$.Comment: 20 pages (LaTeX), CRM-219

A Free Field Representation of the Screening Currents of $U_q(\widehat{sl(3)})

We construct five independent screening currents associated with the $U_q(\widehat{sl(3)})$ quantum current algebra. The screening currents are expressed as exponentials of the eight basic deformed bosonic fields that are required in the quantum analogue of the Wakimoto realization of the current algebra. Four of the screening currents are `simple', in that each one is given as a single exponential field. The fifth is expressed as an infinite sum of exponential fields. For reasons we discuss, we expect that the structure of the screening currents for a general quantum affine algebra will be similar to the $U_q(\widehat{sl(3)})$ case.Comment: 21 pages (LaTeX), CRM-126

From quantum affine groups to the exact dynamical correlation function of the Heisenberg model

The exact form factors of the Heisenberg models $XXX$ and $XXZ$ have been recently computed through the quantum affine symmetry of $XXZ$ model in the thermodynamic limit. We use them to derive an exact formula for the contribution of two spinons to the dynamical correlation function of $XXX$ model at zero temperature.Comment: 5 pages, Latex, Presented at the Symposium ``Exactly soluble models in statistical mechanics: historical perspectives and current status" March 30-31, 1996, Northeastern University, Bosto