论文标题
在其参数的任意值下，对顶点函数的UV和IR无差计算
UV and IR divergence-free calculation of the vertex function at arbitrary values of its arguments
论文作者
论文摘要
使用协变光谱正则化分析顶点函数，而不会遇到任何紫外线或IR差异。描述了在Minkowski空间的开放子集上使用一个Lorentz指数的协方差矩阵衡量标准的协变光谱正则化数学。然后将其应用于顶点函数的情况下，并获得与T通道中与顶点函数相关的密度的表达式，并获得了Minkowski空间上的Lebesgue Measure相对于S通道的表达式。这些密度是对其定义领域的明确定义，无分解和分析性的，并且在不使用重新归一化或需要考虑最终状态辐射的情况下获得。计算在低能和低动量时T通道中顶点函数的表达限，从而导致对电子的异常磁矩的前列级（LO）贡献的经典结果。同样，S通道中顶点函数的密度用于计算该过程的横截面高能量限制的LO顶点校正贡献$ e^{+} e^{ - } \rightArrowμ^{+}+}μ^{ - } $。
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 $e^{+}e^{-}\rightarrowμ^{+}μ^{-}$.
