标题： 重整化规范理论中的复兴与自完成 显示英文标题

标题： Resurgence and self-completion in renormalized gauge theories

摘要： 在某些假设下，并且独立于瞬子，我们证明量子场论中维度正则化的对数展开需要一个非微扰的补全，以使重整化群流在所有能量下都有效。 然后，我们证明这种非微扰补全具有重整子的解析性质，我们无需参考图解计算就发现了这些性质。 我们证明重整子修正必然导致可分析的函数，即渐进超越的级数。 提供了对重整子渐进性质的详细分析。 理论的自洽性要求这些非微扰贡献使运行耦合在任何能量下都定义良好，从而没有兰道极点。 我们在QED的情况下说明了这一点。 这样，我们明确实现了非微扰兰道极点尺度与重整子之间的对应关系。 在微扰理论中被视为兰道极点的现象，被非微扰的、渐进超越的贡献所修复。 显示英文摘要

摘要： Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization-group flow valid at all energies. Then, we show that such nonperturbative completion has the analytic properties of the renormalons, which we find with no reference to diagrammatic calculations. We demonstrate that renormalon corrections necessarily lead to analyzable functions, namely, resurgent transseries. A detailed analysis of the resurgent properties of the renormalons is provided. The self-consistency of the theory requires these nonperturbative contributions to render the running coupling well-defined at any energy, thus with no Landau pole. We illustrate the point within the case of QED. This way, we explicitly realize the correspondence between the nonperturbative Landau pole scale and the renormalons. What is seen as a Landau pole in perturbation theory is cured by the nonperturbative, resurgent contributions.