Leading log expansion of combinatorial Dyson Schwinger equations

管状结构、弦图与Dyson--Schwinger方程

Tubings, chord diagrams, and Dyson--Schwinger equations

本文利用有根树的二元管状结构，求解了更一般的单插入位传播子型Dyson--Schwinger方程组，获得了组合透明的级数解，并讨论了其组合联系与性质。

The full Schwinger-Dyson tower for random tensor models

We treat random rank-$D$ tensor models as $D$-dimensional quantum field theories---tensor field theories (TFT)---and review some of their non-perturbative methods. We classify the correlation functions of complex tensor field theories by boundary graphs, sketch the derivation of the Ward-Takahashi identity and stress its relevance in the derivation of the tower of exact, analytic Schwinger-Dyson equations for all the correlation functions (with connected boundary) of TFTs with quartic pillow-like interactions.

Generalized chord diagram expansions of Dyson-Schwinger equations

Series solutions for a large family of single equation Dyson-Schwinger equations are given as expansions over decorated rooted connected chord diagrams. The analytic input to the new expansions are the expansions of the regularized integrals for the primitive graphs building the Dyson-Schwinger equation. Each decorated chord diagram contributes a weighted monomial in the coefficients of the expansions of the primitives and so indexes the analytic solution in a tightly controlled way.

A chord diagram expansion coming from some Dyson-Schwinger equations

We give an expression for the solution to propagator-type Dyson-Schwinger equations with one primitive at 1 loop as an expansion over rooted connected chord diagrams. Along the way we give a refinement of a classical recurrence of rooted connected chord diagrams, and a representation in terms of binary trees.

具有多个插入位置的 Dyson--Schwinger 方程的代数结构

The algebraic structure of Dyson--Schwinger equations with multiple insertion places

本文利用有根树的管状结构，给出了具有多个插入位置的 Dyson--Schwinger 方程的组合受控级数解，并研究了此类解与重整化群方程之间的代数关系。