论文标题
在$ 4D $上含义的正规化和与维度方法的连接中，仪表理论的两环重归其化
Two-loop renormalisation of gauge theories in $4D$ Implicit Regularisation and connections to dimensional methods
论文作者
论文摘要
我们使用背景场方法在使用隐式正则化（IREG）中使用背景字段方法计算标量和旋转量子电动力学以及纯阳性和量子铬动力学的两环$β$函数。此外，提出了与常规维度正则化（CDR）和尺寸还原（DRED）等维度方法的彻底比较。在IREG中仔细讨论了与Lorentz代数收缩/对称整合以及重新施加方案中有关的微妙之处，在IREG中，仔细讨论了重生常数为基本的差异积分与任意循环顺序的基本分歧积分。此外，我们证实了以下假设：通过将明确定义的表面术语设置为零以零的方式实现的Feynman图循环中的动量路由不变性在IREG内提供了非阿贝尔仪表不变的振幅，就像已证明是为Abelian Theories所证明的那样。
We compute the two-loop $β$-function of scalar and spinorial quantum electrodynamics as well as pure Yang-Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using Implicit Regularization (IREG). Moreover, a thorough comparison with dimensional approaches such as conventional dimensional regularization (CDR) and dimensional reduction (DRED) is presented. Subtleties related to Lorentz algebra contractions/symmetric integrations inside divergent integrals as well as renormalisation schemes are carefully discussed within IREG where the renormalisation constants are fully defined as basic divergent integrals to arbitrary loop order. Moreover, we confirm the hypothesis that momentum routing invariance in the loops of Feynman diagrams implemented via setting well-defined surface terms to zero deliver non-abelian gauge invariant amplitudes within IREG just as it has been proven for abelian theories.
