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

Ling-Lie Chau·Itaru Yamanaka
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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.

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Ling-Lie Chau, Itaru Yamanaka. 1995-12-17. Bi-module Properties of Group-Valued Local Fields and Quantum-Group Difference Equations. https://doi.org/10.1016/0370-2693(95)01553-1

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