Quantum Yang-Mills field theory

TL;DR

This paper presents an exact solution to the Dyson-Schwinger equations for Yang-Mills theory up to the two-point function, demonstrating the existence of correlation functions and a mass gap.

Contribution

It provides an exact analytical solution to the Dyson-Schwinger equations for Yang-Mills theory, maintaining translation invariance and proving the existence of correlation functions.

Findings

Correlation functions exist in Yang-Mills theory.

The two-point function exhibits a mass gap.

The solution maintains translation invariance.

Abstract

We show that the Dyson-Schwinger set of equations for the Yang-Mills theory can be exactly solved till the two-point function. This is obtained given a set of nonlinear waves solving the classical equations of motion. Translation invariance is maintained by the proper choice of the solution of the equation for the two-point function as devised by Coleman. The computation of the Dyson-Schwinger equations is performed in the same way as devised by Bender, Milton and Savage providing a set of partial differential equations whose proof of existence of the solutions is standard. So, the correlation functions of the theory could be proved to exist and the two-point function manifests a mass gap.