A study of the influence of the gauge group on the Dyson-Schwinger equations for scalar-Yang-Mills systems

TL;DR

This paper investigates how the choice of gauge group and matter field representation affects the Dyson-Schwinger equations in scalar-Yang-Mills systems, revealing structural differences that influence the qualitative behavior of the theory.

Contribution

It provides a detailed analysis of the influence of gauge group and matter representation on Dyson-Schwinger equations, offering insights for improved truncation schemes.

Findings

Differences in Dyson-Schwinger equations depending on gauge group and matter representation.

Structural variations in correlation functions linked to gauge choices.

Implications for numerical and analytical approaches in gauge theories.

Abstract

The particular choice of the gauge group for Yang-Mills theory plays an important role when it comes to the influence of matter fields. In particular, both the chosen gauge group and the representation of the matter fields yield structural differences in the quenched case. Especially, the qualitative behavior of the Wilson potential is strongly dependent on this selection. Though the algebraic reasons for this observation is clear, it is far from obvious how this behavior can be described besides using numerical simulations. Herein, it is investigated how the group structure appears in the Dyson-Schwinger equations, which as a hierarchy of equations for the correlation functions have to be satisfied. It is found that there are differences depending on both the gauge group and the representation of the matter fields. This provides insight into possible truncation schemes for practical calculations using these equations.