空间正则化单圈积分的有限表示
On Finite Representation of Dimensionally Regularized One-loop Integrals
摘要：
在量子场论的重整化中，欧氏动量空间积分的维数正则化是一种非常成功的方法。虽然它产生了一个简单的算法方法，用它来评估树级以外的图，但实际的积分可能是高度发散的，至少在传统意义上是这样。特别是，标准的单圈积分可以表示在一个明确的公式，它关联的紫外线和红外发散参数值解析连续的特殊函数表达式。我们的目的是讨论相应的解析连续结构的有限积分表达式的制定。有效地，我们希望建立的条件，形成一个等价类的分析延续，或者说，形成一个适当的设置/条件的正则化技术导致it. This进一步证明，考虑部分和完全成功的战略并排，主要强调两个最简单的功能计划：高斯和截止正则化。通过显式计算，我们的目标是将这些概括的初始积分与维正则化的结果，考虑多个质量（或动量）尺度以及无标度的情况下。我们实现了有限的追求后的积分，通过应用这些合适的计划之一，以及一个额外的计划相关的规模。这使我们能够通过一个算子用附加的尺度去除所有多余的项来设计维度正则化表达式（或局部描述）的适当表示。
英文摘要：
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond tree level, the actual integrals can be highly divergent, at least in a traditional sense. In particular, standard one-loop integrals can be expressed in terms of an explicit formula, which associates both ultraviolet and infrared divergent parameter values to analytically continued special function expressions. We aim to discuss the formulation of finite integral expressions corresponding to the analytically continued structures. Effectively, we wish to establish conditions which form an equivalence class for this analytical continuation, or rather form a proper set/conditions of regularization techniques leading to it. This is further demonstrated by considering both partially and fully successful strategies side-by-side, with major emphasis on the two simplest functioning schemes: Gaussian and cut-off regularization. By explicit computations we aim to associate these generalisations of the initial integrals with the results from dimensional regularization, considering both multiple mass (or momentum) scales as well as scaleless cases. We achieve the finiteness of the sought-after integrals by applying one of these suitable schemes along with an additional scheme related scale. This enables us to devise a proper representation of the dimensionally regularized expressions (or a local description) through an operator removing all excess terms with the additional scale(s).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
