AI 中文总结
研究李群\(G\)上量子动力学，通过构建路径积分来处理非交换动量空间和紧致方向，利用极大环面中绕数求和处理紧致性，计算了欧拉 - 阿诺德系统传播子和配分函数的半经典近似至两圈阶。
AI 中文摘要
我们继续在arXiv:2512.19840中开始的对李群\(G\)上量子动力学的研究，通过构建支配希尔伯特空间\(L^2(G)\)中跃迁振幅的路径积分。这依赖于对非交换动量空间和\(G\)中紧致方向的恰当处理。我们表明紧致性可通过\(G\)的极大环面中绕数求和来处理，推广了圆上路径积分常见的类似求和。作为应用，我们计算了欧拉 - 阿诺德系统传播子和配分函数的半经典近似，直至（并包括）两圈阶。
英文摘要
We continue our study of quantum dynamics on a Lie group $G$, initiated in arXiv:2512.19840, by building the path integral that governs transition amplitudes in the Hilbert space $L^2(G)$. This relies on the proper handling of both a noncommutative momentum space and the presence of compact directions in $G$. We show that compactness can be handled through a sum over winding numbers in maximal tori of $G$, generalizing the similar sum commonly encountered for path integrals on a circle. As applications, we compute semiclassical approximations of propagators and partition functions of Euler-Arnold systems, up to (and including) two-loop order.
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