The computation of observables in general interacting theories, be them quantum mechanical, field, gauge or string theories, is a non-trivial problem which in many cases can only be addressed by resorting to perturbative methods. In most physically interesting problems these perturbative expansions result in asymptotic series with zero radius of convergence. These asymptotic series then require the use of resurgence and transseries in order for the associated observables to become nonperturbatively well-defined. Resurgence encodes the complete large-order asymptotic behaviour of the coefficients from a perturbative expansion, generically in terms of (multi) instanton sectors and for each problem in terms of its Stokes constants. Some observables arise from linear problems, and have a finite number of instanton sectors and associated Stokes constants; some other observables arise from nonlinear problems, and have an infinite number of instanton sectors and Stokes constants. By means of two very explicit examples, and with emphasis on a pedagogical style of presentation, this work aims at serving as a primer on the aforementioned resurgent, large-order asymptotics of general perturbative expansions. This includes discussions of transseries, Stokes phenomena, generalized steepest-descent methods, Borel transforms, nonlinear resonance, and alien calculus. Furthermore, resurgent properties of transseries---usually described mathematically via alien calculus---are recast in equivalent physical languages: either a "statistical mechanical" language, as motions in chains and lattices; or a "conformal field theoretical" language, with underlying Virasoro-like algebraic structures.

中文翻译：

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Resurgent transseries 及其渐近线入门

在一般的相互作用理论中计算可观察量，无论是量子力学、场、规范或弦理论，都是一个重要的问题，在许多情况下只能通过采用微扰方法来解决。在大多数物理有趣的问题中，这些微扰扩展会导致收敛半径为零的渐近级数。然后，这些渐近级数需要使用回潮和超序列，以便相关联的可观察量变得非扰动明确定义。Resurgence 对来自微扰展开的系数的完整大阶渐近行为进行编码，一般根据（多）瞬时子扇区和每个问题的斯托克斯常数。一些可观察量来自线性问题，并且具有有限数量的瞬时扇区和相关的斯托克斯常数；其他一些可观察量来自非线性问题，并且具有无限数量的瞬时子扇区和斯托克斯常数。通过两个非常明确的例子，并强调教学风格的呈现，这项工作旨在作为上述复苏的一般微扰展开的大阶渐近的入门。这包括对超串联、斯托克斯现象、广义最速下降法、Borel 变换、非线性共振和外星微积分的讨论。此外，反序列的复活特性——通常通过外星微积分在数学上描述——用等效的物理语言重新定义：要么是“统计力学”语言，如链和格子中的运动；或“