论文标题
Minkowski空间中的双共形盒积分
The Dual Conformal Box Integral in Minkowski Space
论文作者
论文摘要
Minkowski空间中的双共构盒积分不可能完全由Condomatal Infortiants $ z $和$ \ bar {z} $确定。根据运动学区域的不同，其值在欧几里得情况下发生的Bloch-Wigner函数的“分支”。 Minkowski空间中的双重特殊共形变换可以以某种方式改变运动区域，以使积分的值跳到此功能的另一个分支，编码整数的双重构造不变性的细微破坏。我们在压实的Minkowski空间中对四个点的共形等效构型进行了分类。我们表明，从任何配置开始，都可以使用双重共形变换来达到积分的四个分支。我们还表明，大多数具有真实$ z $和$ \ bar {z} $的配置可以合并地映射到同一运动区域中的配置，在Infinity处有两个点，可以在Minkowski空间中直接使用残基定理在Minkowski空间中直接计算盒子积分。
The dual conformal box integral in Minkowski space is not fully determined by the conformal invariants $z$ and $\bar{z}$. Depending on the kinematic region its value is on a 'branch' of the Bloch-Wigner function which occurs in the Euclidean case. Dual special conformal transformations in Minkowski space can change the kinematic region in such a way that the value of the integral jumps to another branch of this function, encoding a subtle breaking of dual conformal invariance for the integral. We classify conformally equivalent configurations of four points in compactified Minkowski space. We show that starting with any configuration, one can reach up to four branches of the integral using dual special conformal transformations. We also show that most configurations with real $z$ and $\bar{z}$ can be conformally mapped to a configuration in the same kinematic region with two points at infinity, where the box integral can be calculated directly in Minkowski space using only the residue theorem.
