Abstract Expansions of physical functions are controlled by their singularities, which have special structure because they themselves are physical, corresponding to instantons, caustics or saddle configurations. Resurgent asymptotics formalizes this idea mathematically, and leads to significantly more powerful extrapolation methods to extract physical information from a finite number of terms of an expansion, including precise decoding of non-perturbative effects. We quantify the gain of precision for various extrapolation procedures, showing that significant improvements can be achieved using exactly the same input data, and we illustrate the general method with examples from quantum mechanics and quantum field theory.

中文翻译：

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物理复苏外推

摘要 物理函数的展开受奇点控制，奇点具有特殊的结构，因为它们本身是物理的，对应于瞬子、焦散或鞍座配置。Resurgent asymptotics 在数学上形式化了这个想法，并导致显着更强大的外推方法从有限数量的扩展项中提取物理信息，包括对非微扰效应的精确解码。我们量化了各种外推程序的精度增益，表明使用完全相同的输入数据可以实现显着的改进，并且我们通过量子力学和量子场论的示例说明了一般方法。