Quantum Yang-Mills field theory

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.

15 pages, no figure. Version accepted for publication in European Physical Journal Plus

References in corpus (5)

• Infrared Gluon and Ghost Propagators
• Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case
• Scalar field theory in the strong self-interaction limit
• Self-interacting scalar fields at high-temperature
• Exact solutions for classical Yang-Mills fields

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