标题： 圈振幅的自相似结构与重整化 显示英文标题

标题： Self-Similar Structure of Loop Amplitudes and Renormalization

摘要： 我们研究了量子场论中圈振幅的自相似结构，并将其应用于振幅生成和重整化。 一个重整化的振幅可以被视为有效耦合，它递归地出现在另一个圈中。 它最好被描述为来自有效作用量的顶点函数。 它是出现在S矩阵中的标度相关、有限、参数上较小且可观测的量。 用圈振幅替换树级耦合提供了一种系统的方法来生成高阶圈振幅，并保证没有子振幅发散。 该方法还提供了传统自顶向下递归重整化的一种替代自下而上的证明。 显示英文摘要

摘要： We study the self-similar structure of loop amplitudes in quantum field theory and apply it to amplitude generation and renormalization. A renormalized amplitude can be regarded as an effective coupling that recursively appears within another loop. It is best described as a vertex function from the effective action. It is a scale-dependent, finite, parametrically small and observable quantity appearing in the S-matrix. Replacing a tree-level coupling with a loop amplitude provides a systematic method of generating high-order loop amplitudes, guaranteeing no subamplitude divergence. This method also provides an alternative bottom-up proof to the traditional top-down recursive renormalization of general amplitudes.