论文标题
走向有限的量子场理论
Towards the finite quantum field theory
论文作者
论文摘要
在这项研究中，我们提出了一种利用辅助Feynman参数化的新型正则化/重新归一化方案。使用此方法将指定的环图与表格$ 1 =λ/λ$的指定单位对齐。在提出的正则化技术中，我们制定了标准的重新归一化方案，并证明了它得出对称性保留结果的条件。证明其最小形式产生的重新归一化图等效于尺寸重新归一化方案的图，除了它们的对抗。此外，采用软限制$λ\ rightarrow 0 $的新型程序，其中正确定义的计算作用顺序提供了完全有限的场理论。该方法与标准方案之间的定性和定量区别都得到了强调。出于教学原因，在标量模型中以3+1D阐明了这两种方案。随后，提出的方案将在一个循环级别上应用于标准模型，例如我们计算光子和Gluon极化。 QCD有效电荷是在有限的QCD中计算出来的，表现出明确的证据，表明未排除有限的QCD，而是由实验支持。在最后一部分中，我们提供了关于柔软异常的软化和对差异重叠差异的处理的简洁讨论，并附有说明性的例子。
In this study, we propose a novel regularization/renormalization scheme that utilizes an auxiliary Feynman parameterization. This approach is employed to align a specified loop diagram with a designated unit of the form $1=λ/λ$. Within the proposed regularization technique, we formulate the standard renormalization scheme and demonstrate conditions under which it yields symmetry preserving results. It is demonstrated that its minimal form yields renormalized diagrams that are equivalent to those of the dimensional renormalization scheme, with the exception of their counterterms. Furthermore, a novel procedure for taking the soft limit $λ\rightarrow 0$, where a properly defined order of computational actions provides the field theory completely finite, is presented.The qualitative and quantitative distinctions between this approach and the standard scheme are highlighted. Both schemes are elucidated in the scalar model in 3+1D for pedagogical reasons. Subsequently, the proposed schemes are applied to the Standard Model at one loop level, e.g. we calculate photon and gluon polarizations. QCD effective charge is calculated in the finite QCD, exhibiting a clear evidence that the finite QCD is not ruled out but supported by experiment. In the final section, we offer a concise discussion on the softening of anomalies and the treatment of overlapping divergences, accompanied by illustrative examples.
