Bi-module Properties of Group-Valued Local Fields and Quantum-Group Difference Equations

Abstract

We give an explicit construction of the quantum-group generators ---local, semi-local, and global --- in terms of the group-valued quantum fields $\tilde{g}$ and ${\tilde{g}}^{-1}$ in the Wess-Zumino-Novikov-Witten (WZNW) theory. The algebras among the generators and the fields make concrete and clear the bi-module properties of the $\tilde{g}$ and the ${\tilde{g}}^{-1}$ fields. We show that the correlation functions of the $\tilde{g}$ and ${\tilde{g}}^{-1}$ fields in the vacuum state defined through the semi-local quantum-group generator satisfy a set of quantum-group difference equations. We give the explicit solution for the two point function. A similar formulation can also be done for the quantum Self-dual Yang-Mills (SDYM) theory in four dimensions.

12 pages; uses latex; minor revisions for publication in Phys. Lett. B

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