Free Boson Representation of $q$-Vertex Operators and their Correlation Functions

TL;DR

This paper develops a bosonization scheme for q-vertex operators of quantum affine algebra, providing integral formulas for N-point functions and explicit two-point function calculations.

Contribution

It introduces a bosonization scheme for q-vertex operators at arbitrary level, enabling explicit computation of correlation functions.

Findings

Bosonization scheme for q-vertex operators at any level.

Integral formula for N-point functions.

Explicit two-point function calculation.

Abstract

A bosonization scheme of the $q$-vertex operators of $\uqa$ for arbitrary level is obtained. They act as intertwiners among the highest weight modules constructed in a bosonic Fock space. An integral formula is proposed for $N$-point functions and explicit calculation for two-point function is presented.