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

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

The K-Z Equation and the Quantum-Group Difference Equation in Quantum Self-dual Yang-Mills Theory

From the time-independent current \tcj(\bar y,\bar k) in the quantum self-dual Yang-Mills (SDYM) theory, we construct new group-valued quantum fields $\tilde U(\bar y,\bar k)$ and $\bar U^{-1}(\bar y,\bar k)$ which satisfy a set of exchange algebras such that fields of \tcj(\bar y,\bar k)\sim\tilde U(\bar y,\bar k)~\partial\bar y~\tilde U^{-1}(\bar y,\bar k) satisfy the original time-independent current algebras. For the correlation functions of the products of the $\tilde U(\bar y,\bar k)$ and $\tilde U^{-1}(\bar y,\bar k)$ fields defined in the invariant state constructed through the current \tcj(\bar y,\bar k) we can derive the Knizhnik-Zamolodchikov (K-Z) equations with an additional spatial dependence on $\bar k$. From the $\tilde U(\bar y,\bar k)$ and $\tilde U^{-1}(\bar y,\bar k)$ fields we construct the quantum-group generators --- local, global, and semi-local --- and their algebraic relations. For the correlation functions of the products of the $\tilde U$ and $\tilde U^{-1}$ fields defined in the invariant state constructed through the semi-local quantum-group generators we obtain the quantum-group difference equations. We give the explicit solution to the two point function.Comment: 15 pages, uses phyzz

Lingnan campus opening

The opening of Lingnan College’s new campus in Tuen Mun on February 14, 1996 marked an important stage in the college’s development and was a significant step towards its goal of becoming a fully residential liberal arts university.https://commons.ln.edu.hk/lingnan_milestone_newspapers/1004/thumbnail.jp

Conformal Symmetries of the Self-Dual Yang-Mills Equations

We describe an infinite-dimensional Kac-Moody-Virasoro algebra of new hidden symmetries for the self-dual Yang-Mills equations related to conformal transformations of the 4-dimensional base space.Comment: 12 pages, Late

Inverse Avalanches On Abelian Sandpiles

A simple and computationally efficient way of finding inverse avalanches for Abelian sandpiles, called the inverse particle addition operator, is presented. In addition, the method is shown to be optimal in the sense that it requires the minimum amount of computation among methods of the same kind. The method is also conceptually nice because avalanche and inverse avalanche are placed in the same footing.Comment: 5 pages with no figure IASSNS-HEP-94/7

Correcting Quantum Errors In Higher Spin Systems

I consider the theory of quantum error correcting code (QECC) where each quantum particle has more than two possible eigenstates. In this higher spin system, I report an explicit QECC that is related to the symmetry group ${\Bbb Z}_2^{\otimes (N-1)} \otimes S_N$. This QECC, which generalizes Shor's simple majority vote code, is able to correct errors arising from exactly one quantum particle. I also provide a simple encoding algorithm.Comment: In REVTEX 3.0, requires AMS fonts. Typos corrected. To appear in PRA (Rapid Comm.