论文标题
暴露循环积分的阈值结构
Exposing the threshold structure of loop integrals
论文作者
论文摘要
对确定振幅红外行为的物理定律的理解是一个长期存在的问题。在本文中，我们表明，仅节能就意味着对Feynman图的阈值奇异性结构的强烈限制。特别是，我们表明它暗示着循环积分的表示，而不是近似凸锥的傅立叶变换。然后，我们设计了一个三角剖分，该三角剖分在直接的边缘接收操作方面具有直接的图解解释。我们使用它来开发一种算法程序，该过程以封闭形式执行傅立叶积分，从而产生了环路积分的新型跨族家庭三维表示。与TOPT和LTD表示相反，其奇异性结构完全优雅地表达了连接性和交叉的图理论概念。这些结果可用于分类红外线散射理论，数值评估循环积分并简化阈值正则化过程。
The understanding of the physical laws determining the infrared behaviour of amplitudes is a longstanding and topical problem. In this paper, we show that energy conservation alone implies strong constraints on the threshold singularity structure of Feynman diagrams. In particular, we show that it implies a representation of loop integrals in terms of Fourier transforms of non-simplicial convex cones. We then engineer a triangulation that has a direct diagrammatic interpretation in terms of a straightforward edge-contraction operation. We use it to develop an algorithmic procedure that performs the Fourier integrations in closed form, yielding the novel Cross-Free Family three-dimensional representation of loop integrals. Contrary to the TOPT and LTD representations, its singularity structure is entirely and elegantly expressed in terms of the graph-theoretic notions of connectedness and crossing. These results can be used to classify infrared-finite scattering theories, numerically evaluate loop integrals and to simplify threshold regularisation procedures.
