Landau方程对迭代积分的意义
Implications of the Landau Equations for Iterated Integrals
摘要：
本文介绍了一种从朗道轨迹附近的费曼积分的渐近展开式导出费曼积分符号约束的方法。特别是，我们表明，这些积分附近的奇点的行为是直接相关的符号中的字母之一消失或成为无限的位置。我们说明了这种方法的积分与一般的质量，并作为推论证明了超越重量的多对数$\ell$ -环积分的$\lfloor \frac {D \ell} 2\rfloor$的约束，这种类型的整数维数$D$。我们还推导出新的约束的运动学依赖的某些产品的符号字母，保持有限的奇异点附近。
英文摘要：
We introduce a method for deriving constraints on the symbol of Feynman integrals from the form of their asymptotic expansions in the neighborhood of Landau loci. In particular, we show that the behavior of these integrals near singular points is directly related to the position in the symbol where one of the letters vanishes or becomes infinite. We illustrate this method on integrals with generic masses, and as a corollary prove the conjectured bound of $\lfloor \frac {D \ell} 2\rfloor$ on the transcendental weight of polylogarithmic $\ell$-loop integrals of this type in integer numbers of dimensions $D$. We also derive new constraints on the kinematic dependence of certain products of symbol letters that remain finite near singular points.
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