论文标题
关于量子场理论中的枚举结构
On the Enumerative Structures in Quantum Field Theory
论文作者
论文摘要
本文解决了在量子场理论和重新规定过程中出现的许多列举问题。特别是，进一步研究了根系连接的和弦图的枚举，并引入了淬火QED和Yukawa理论中的新应用。和弦图出现在量子场理论中，在戴森 - 辛格方程式的背景下，根据最近的结果，它们用于表达解决方案。在另一个方向上，我们研究了点场差异对自由理论的作用。我们给出了有关转化理论的树级振幅消失现象的新证明。
This thesis addresses a number of enumerative problems that arise in the context of quantum field theory and in the process of renormalization. In particular, the enumeration of rooted connected chord diagrams is further studied and new applications in quenched QED and Yukawa theories are introduced. Chord diagrams appear in quantum field theory in the context of Dyson-Schwinger equations, where, according to recent results, they are used to express the solutions. In another direction, we study the action of point field diffeomorphisms on a free theory. We give a new proof of a vanishing phenomenon for tree-level amplitudes of the transformed theories.
