From quantum Bäcklund transforms to topological quantum field theory
From quantum Bäcklund transforms to topological quantum field theory
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从量子贝克伦德变换到拓扑量子场论
DOI：
10.1088/1751-8113/49/10/104001
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
C. Korff
中科院分区：
文献类型：
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作者：
C. Korff
我们推导出量子化的Ablowitz-Ladik链的Bäcklund变换的量子模拟，非线性薛定谔方程的空间离散化。阿布洛维茨-拉迪克链的量子化导致了q玻色子模型。利用作者以前对这一模型构造的巴克斯特Q算子，得到了一组函数关系，它将一个单变量经典Bäcklund变换的关系匹配到该模型的所有阶。.我们还构造了第二个Q算子，并证明了它与第一个Q算子的逆算子密切相关。从Q算子产生的多Bäcklund变换定义了二维TQFT的融合矩阵，我们推导出一个线性系统，用于解决量子Bäcklund关系的TQFT融合系数。
We derive the quantum analogue of a Bäcklund transformation for the quantized Ablowitz–Ladik chain, a space discretization of the nonlinear Schrödinger equation. The quantization of the Ablowitz–Ladik chain leads to the q-boson model. Using a previous construction of Baxter’s Q-operator for this model by the author, a set of functional relations is obtained which matches the relations of a one-variable classical Bäcklund transform to all orders in ℏ ?> . We construct also a second Q-operator and show that it is closely related to the inverse of the first. The multi-Bäcklund transforms generated from the Q-operator define the fusion matrices of a 2D TQFT and we derive a linear system for the solution to the quantum Bäcklund relations in terms of the TQFT fusion coefficients.