关于高阶施瓦茨导数的若干注记
Remarks on higher Schwarzians
AI总结：
本文将 Bertilsson 的高阶施瓦茨导数与 l-共形伽利略群建立联系，并揭示其递推关系、复合律和对称变换等性质，为高阶施瓦茨导数的物理应用奠定基础。
摘要：
施瓦茨导数近来因 Sachdev-Ye-Kitaev 模型的研究而重新受到关注。在数学文献中，Aharonov、Bertilsson 和 Schippers 已给出施瓦茨导数的多种高阶推广。高阶施瓦茨导数的物理应用尚未被详细讨论。本文中，我们将 Bertilsson 的变体与 l-共形伽利略群联系起来，并讨论其若干有趣特性，包括一个递推关系（可迭代构造高阶施瓦茨导数）、一个复合律以及对称变换。
英文摘要：
The Schwarzian derivative has recently received renewed attention in connection with the study of the Sachdev-Ye-Kitaev model. In mathematics literature, various higher order generalizations of the Schwarzian derivative are known due to Aharonov, Bertilsson, and Schippers. Physical applications of the higher Schwarzian derivatives have not yet been discussed in any detail. In this work, we link Bertilsson's variant to the l-conformal Galilei group, as well as discuss some of its interesting peculiarities. These include a recurrence relation, which allows one to construct the higher Schwarzians iteratively, a composition law, and symmetry transformations.
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