Eur. Phys. J. Plus (2017) 132: 38
https://doi.org/10.1140/epjp/i2017-11321-4

Regular Article

Quantum Yang-Mills field theory

Via Erasmo Gattamelata, 3, 00176, Rome, Italy

^* e-mail: marcofrasca@mclink.it

Received: 20 June 2016
Accepted: 27 December 2016
Published online: 24 January 2017

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.