具有动力学边界的时间依赖可积量子场论
Time-dependent integrable quantum field theories with dynamical boundaries
- University of Geneva（日内瓦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出从自治可积模型的散射与反射数据构造时间依赖可积手征量子场论的方法，通过仿射谱坐标统一体与边界驱动，并导出边界qKZ方程，重构局部哈密顿量，以SU(N)和O(3)模型示例验证。
AI中文摘要：
我们提出了一种方法，用于从自治可积模型的散射和反射数据出发，在有限空间区间上构造时间依赖的可积手征量子场论。每个粒子携带一个谱标签，该标签在其自由轨迹上保持不变。要求固定时刻的左右散射事件与其位置无关，这迫使从特征坐标到谱标签的映射是仿射的，且两种手征性具有相同的斜率。因此，在给定时刻的所有体散射事件都采样一个共同的谱参数，而两个边界反射则采样相应的端点参数。体驱动和边界驱动并非独立的时间依赖形变：它们的时间依赖性由同一个仿射谱坐标固定。在两个端点处的连续反射会将谱标签平移有限量。随后，跟踪一个粒子完成一次完整往返，会产生一个差分输运，其一致性给出了边界量子Knizhnik--Zamolodchikov方程。Yang--Baxter方程和反射方程确保了局部相容性，而BqKZ平坦性确保了完整往返的相容性。然后，我们通过反转单粒子和双粒子匹配问题来重构局部哈密顿量。体矩阵确定了接触相互作用，而反射矩阵确定了相应的边界耦合。相同的自治因子化数据决定了边界qKZ输运问题和局部驱动哈密顿量。一旦边界qKZ系统被求解，其特征拉回就给出了相应的时间依赖多体波函数。我们用有理$SU(N)$模型和具有动力学边界杂质的$O(3)$不变模型来说明该构造，获得了驱动Kondo相互作用，其耦合由同一个仿射谱坐标固定。
英文摘要：
We present a method for constructing time-dependent integrable chiral quantum field theories on a finite spatial interval from the scattering and reflection data of an autonomous integrable model. Each particle carries a spectral label that is constant along its free trajectory. Requiring a right--left scattering event at a fixed time to be independent of its position forces the map from characteristic coordinates to spectral labels to be affine, with the same slope for both chiralities. As a result, all bulk scattering events at a given time sample one common spectral argument, and the two boundary reflections sample the corresponding endpoint arguments. The bulk and boundary drives are not independent time-dependent deformations: their time dependence is fixed by the same affine spectral coordinate. Successive reflections at the two endpoints translate the spectral label by a finite amount. Following a particle through a complete round trip then produces a difference transport whose consistency gives the boundary quantum Knizhnik--Zamolodchikov equations. The Yang--Baxter and reflection equations ensure local compatibility, while BqKZ flatness ensures compatibility of complete round trips. We then reconstruct the local Hamiltonian by inverting the one- and two-particle matching problems. The bulk matrix fixes the contact interaction, while the reflection matrix fixes the corresponding boundary coupling. The same autonomous factorized data determine the boundary qKZ transport problem and the local driven Hamiltonian. Once the boundary qKZ system is solved, its characteristic pullback gives the corresponding time-dependent many-body wavefunction. We illustrate the construction with rational $SU(N)$ models and an $O(3)$-invariant model with dynamical boundary impurities, obtaining driven Kondo interactions whose couplings are fixed by the same affine spectral coordinate.
