AI 中文总结
该研究从满足杨-巴克斯特方程的自治幺正差形式S矩阵出发，开发通用流程构造含时可积手征场理论，通过特征线映射等步骤推导非自治相互作用，得到从自治散射数据到含时可积场理论的几何途径。
AI 中文摘要
我们开发了一套通用流程，用于从满足杨-巴克斯特方程的自治幺正差形式S矩阵构造含时可积手征场理论。谱参数沿自由的右行和左行特征线传输，定义了从物理时空到谱空间的映射，两体散射数据在该谱空间上取值。要求空间均匀的右-左散射，会迫使特征线映射为仿射映射。逆凯莱变换确定局域接触相互作用，沿仿射谱轨迹的取值则确定其时间依赖性。因此，非自治相互作用由自治散射数据、手征运动学和空间均匀性共同决定，而非独立引入。杨-巴克斯特方程提供了因子化的多体传输，在空间圆周上，周期性会导出量子 Knizhnik-Zamolodchikov（qKZ）方程，其相容性定义了谱空间中的平坦离散传输。将对应的谱空间振幅拉回物理坐标，便得到含时多体波函数。有理SU(N)、三角U_q(𝔰𝔩̂₂)和有理O(N)散射实例说明，同一机制如何生成不同的非自治相互作用。该框架提供了从自治因子化散射数据到含时可积场理论的几何途径。
英文摘要
We develop a general procedure for constructing time-dependent integrable chiral field theories from autonomous unitary difference-form $S$-matrices satisfying the Yang-Baxter equation. Spectral parameters are transported along the free right- and left-moving characteristics, defining a map from physical spacetime to spectral space on which the two-body scattering data are evaluated. Requiring spatially homogeneous right-left scattering forces the characteristic map to be affine. The inverse Cayley transform then determines the local contact interaction, while evaluation along the affine spectral trajectory fixes its time dependence. Thus, the nonautonomous interaction is determined by the autonomous scattering data together with chiral kinematics and spatial homogeneity, rather than being introduced independently. The Yang--Baxter equation supplies the factorized many-body transport, and on a spatial circle periodicity leads to quantum Knizhnik--Zamolodchikov (qKZ) equations whose compatibility defines a flat discrete transport in spectral space. Pulling the corresponding spectral-space amplitudes back to physical coordinates gives the time-dependent many-body wavefunctions. Rational $SU(N)$, trigonometric $U_q(\widehat{\mathfrak{sl}}_2)$, and rational $O(N)$ scattering illustrate how the same mechanism generates distinct nonautonomous interactions. The resulting framework gives a geometric route from autonomous factorized scattering data to time-dependent integrable field theories.
