论文标题
面向流动的扰动理论
Flow-oriented perturbation theory
论文作者
论文摘要
我们引入了一种新的图解方法来扰动量子场理论，我们称之为流动的扰动理论（FOPT）。其中，Feynman图被牢固连接的有向图（Digraphs）取代。 FOPT是时间订购的扰动理论和循环树双重性的坐标空间类似，但它具有具有组合和规范的Feynman规则的优势，并结合了所得积分的简化$ i \ varepsilon $依赖性。此外，我们引入了S-Matrix的基于新颖的基于Digraph的表示。相关的积分涉及流层的傅立叶变换。由于该多层的属性，我们的S-矩阵表示在人均水平上表现出明显的红外奇异性分解。我们的发现揭示了虚假奇异性与多面体变换之间的有趣相互作用。
We introduce a new diagrammatic approach to perturbative quantum field theory, which we call flow-oriented perturbation theory (FOPT). Within it, Feynman graphs are replaced by strongly connected directed graphs (digraphs). FOPT is a coordinate space analogue of time-ordered perturbation theory and loop-tree duality, but it has the advantage of having combinatorial and canonical Feynman rules, combined with a simplified $i\varepsilon$ dependence of the resulting integrals. Moreover, we introduce a novel digraph-based representation for the S-matrix. The associated integrals involve the Fourier transform of the flow polytope. Due to this polytope's properties, our S-matrix representation exhibits manifest infrared singularity factorization on a per-diagram level. Our findings reveal an interesting interplay between spurious singularities and Fourier transforms of polytopes.
