Inherent color symmetry of quantum Yang-Mills theory

TL;DR

This paper explores the non-perturbative structure of SU(3) Yang-Mills theory, highlighting the role of the Weyl group in constructing solutions and implications for color confinement in quantum chromodynamics.

Contribution

It introduces a non-perturbative approach using Weyl symmetric solutions to classify classical solutions and establish a stable vacuum structure in Yang-Mills theory.

Findings

Weyl group symmetry leads to new non-perturbative solutions.

A stable non-degenerate vacuum supports color confinement.

Classified solution space is countably infinite.

Abstract

We present the basic non-perturbative structure of the space of classical dynamical solutions and corresponding one particle quantum states in SU(3) Yang-Mills theory. It has been demonstrated that the Weyl group of su(3) algebra plays an important role in constructing non-perturbative solutions and leads to profound changes in the structure of the classical and quantum Yang-Mills theory. We show that the Weyl group as a non-trivial color subgroup of SU(3) admits singlet irreducible representations on a space of classical dynamical solutions which lead to strict concepts of one particle quantum states for gluons and quarks. The Yang-Mills theory is a non-linear theory and, in general, it is not possible to construct a Hilbert space of classical solutions and quantum states as a linear vector space, so, usually, a perturbative approach is applied. We propose a non-perturbative approach based on Weyl symmetric solutions to full non-linear equations of motion and construct a full space of dynamical solutions representing an infinite but countable solution space classified by a finite set of integer numbers. It has been proved that the Weyl singlet structure of classical solutions provides the existence of a stable non-degenerate vacuum which serves as a main precondition of the color confinement phenomenon. Some physical implications in quantum chromodynamics are considered.