发表机构
QMUL（伦敦玛丽女王大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文发现量子场论中Magnus展开的经典极限与排列的Malvenuto-Reutenauer Hopf代数相关，通过三次标量理论计算树级经典Magnus振幅，证明超经典贡献抵消并匹配世界线量子场论，建立了新公式并观察到与web混合矩阵的联系。
AI 中文摘要
我们揭示了量子场论中Magnus展开的经典极限与排列的Malvenuto-Reutenauer Hopf代数之间的联系。我们研究了一个描述有质量粒子耦合到无质量标量量子的三次标量理论，该理论捕捉了与引力及标量QED中经典散射相关的传播子结构。利用有质量传播子的Schwinger参数化，我们在该理论的树级计算了Magnus振幅的经典极限。首先，我们证明了所有超经典贡献在积分之前的Schwinger固有时间被积函数层面上相互抵消。然后，我们展示了经典Magnus振幅与世界线量子场论的预期精确匹配。这两个结果都依赖于不连通图的抵消，我们将这些抵消与Hopf代数联系起来，具体地说是与伴随第一Eulerian投影算子的作用相关，该算子湮灭了与不连通贡献相关联的shuffle乘积。此外，世界线图包括一般的定向树拓扑，而场论图仅包括定向链。因此，我们建立的这两者之间的对应关系引出了一个新公式，用更简单的定向链系数来表示一般的Murua系数。最后，我们观察到Magnus振幅与控制多条Wilson线指数化的web混合矩阵之间存在一种暗示性的联系。
英文摘要
We uncover a connection between the classical limit of the Magnus expansion in quantum field theory and the Malvenuto-Reutenauer Hopf algebra of permutations. We study a cubic scalar theory describing a massive particle coupled to massless scalar quanta, which captures the propagator structure relevant to classical scattering in gravity and scalar QED. Using a Schwinger parametrisation of the massive propagators, we compute the classical limit of Magnus amplitudes at tree level in this theory. First, we prove that all hyperclassical contributions cancel at the level of the Schwinger proper-time integrand, before integration. Then, we show that the classical Magnus amplitude precisely matches expectations from worldline quantum field theory. Both results rely on cancellations of disconnected diagrams which we relate to the Hopf algebra, specifically to the action of the adjoint first Eulerian projector, which annihilates the shuffle products associated with disconnected contributions. Moreover, the worldline diagrams include generic directed-tree topologies, whereas the field-theory diagrams only include directed chains. The correspondence we establish between the two therefore leads to a new formula for generic Murua coefficients in terms of simpler directed chain coefficients. Finally, we observe a suggestive connection between Magnus amplitudes and the web-mixing matrices governing the exponentiation of multiple Wilson lines.
Comments72 pages
