Quantum integrable systems and TQFT

该项目将研究从量子可积系统构建二维拓扑量子场论（TQFT）。前者是用Frobenius代数来描述的，而后者是用非协易的Hopf代数来给出的，所谓的Yang-Baxter代数是用量子Yang-Baxter方程的解来定义的。Bethe ansatz是一种用于对角化量子可积系统的哈密顿量的技术，它可以得到一组描述二维TQFT的非线性方程。

The project will investigate the construction of 2D topological quantum field theories (TQFT) from quantum integrable systems. The former are described in terms of Frobenius algebras, while the latter are given in terms of non-cocommutative Hopf algebras, so-called Yang-Baxter algebras which are defined in terms of solutions to the quantum Yang-Baxter equation. The Bethe ansatz, a technique used to diagonalise the Hamiltonian of the quantum integrable system, leads to a set of nonlinear equations describing a 2D TQFT.