顶点函数在其自变量任意值下的紫外与红外无发散计算
UV and IR divergence-free calculation of the vertex function at arbitrary values of its arguments
AI总结：
本文提出协变谱正则化方法，在无紫外和红外发散下计算顶点函数，得到t通道和s通道的解析密度，并复现电子反常磁矩领头阶及高能截面修正。
摘要：
本文利用协变谱正则化方法分析顶点函数，避免了任何紫外或红外发散。文中描述了在闵可夫斯基空间开子集上，针对带有一个洛伦兹指标的协变矩阵值测度的协变谱正则化的数学原理。随后，将此方法应用于顶点函数情形，并获得了与顶点函数在t通道和s通道中相对于闵可夫斯基空间勒贝格测度的密度表达式。这些密度在其定义域内良定义、无发散且解析，且无需使用重整化或考虑末态辐射即可获得。在低能量和低动量下，t通道顶点函数表达式的极限被计算，得到了电子反常磁矩领头阶（LO）贡献的经典结果。此外，利用s通道顶点函数的密度，计算了过程$e^{+}e^{-}\rightarrow\mu^{+}\mu^{-}$高能极限下截面的领头阶顶点修正贡献。
英文摘要：
The vertex function is analyzed using covariant spectral regularization without encountering any divergence, either UV or IR. The mathematics of covariant spectral regularization for covariant matrix valued measures with one Lorentz index on open subsets of Minkowski space is described. This is then applied to the case of the vertex function and expressions for the densities associated with the vertex function in the t channel and the s channel with respect to Lebesgue measure on Minkowski space are obtained. These densities are well defined, non-divergent and analytic over their domains of definition and are obtained without using renormalization or needing to consider final state radiation. The limit of the expression for the vertex function in the t channel at low energy and low momenta is computed resulting in the classical result for the leading order (LO) contribution to the anomalous magnetic moment of the electron. Also the density for the vertex function in the s channel is used to compute the LO vertex correction contribution to the high energy limit of the cross section for the process $e^{+}e^{-}\rightarrowμ^{+}μ^{-}$.
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