# Differential Dyson-Schwinger equations for quantum chromodynamics

## TL;DR

This paper derives differential Dyson-Schwinger equations for QCD, focusing on two-point functions, and explores their behavior in the large color limit to understand phenomena like chiral symmetry breaking and confinement.

## Contribution

It introduces a differential form of Dyson-Schwinger equations for QCD and analyzes their behavior in the 't Hooft limit, providing insights into low-energy phenomena.

## Key findings

- Large N limit describes low-energy QCD behavior
- Conditions for confinement are discussed
- Chiral symmetry breaking is analyzed

## Abstract

Using a technique devised by Bender, Milton and Savage, we derive the Dyson-Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The 't~Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.