论文标题
Landau和任意时空维度的领导奇点
Landau and leading singularities in arbitrary space-time dimensions
论文作者
论文摘要
利用将$ d $二维的时空分解为并联和垂直子空间，我们通过应用多维残基的多维理论来研究并证明了Landau与$ n $ n $ n $ n $ n $ nloop Feynman积分之间的联系。我们表明，如果$ d = n $和$ d = n+1 $，则领先的奇异性分别对应于第一类和第二类的领先兰道奇点的平方根的倒数。我们利用这种结果来系统地提供典型形式的Feynman积分的微分方程，并通过利用逐环方法来扩展这些奇异性在多环级别的连接。提供了Landau和领先奇点的计算的说明性示例，以补充我们的结果。
Using the decomposition of the $D$-dimensional space-time into parallel and perpendicular subspaces, we study and prove a connection between Landau and leading singularities for $N$-point one-loop Feynman integrals by applying multi-dimensional theory of residues. We show that if $D=N$ and $D=N+1$, the leading singularity corresponds to the inverse of the square root of the leading Landau singularity of the first and second type, respectively. We make use of this outcome to systematically provide differential equations of Feynman integrals in canonical forms and the extension of the connection of these singularities at multi-loop level by exploiting the loop-by-loop approach. Illustrative examples with the calculation of Landau and leading singularities are provided to supplement our results.
