Inherent color symmetry in quantum Yang-Mills theory

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.(c) 2023 Published by Elsevier B.V. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.

Automated summary

We present the basic non-perturbative structure of classical dynamical solutions and one particle quantum states in SU(3) Yang-Mills theory. The Weyl group of su(3) algebra plays a crucial role in constructing these solutions and has profound effects on the structure of the classical and quantum Yang-Mills theory. Our study reveals that the Weyl group allows for singlet irreducible representations on the space of classical dynamical solutions, which provides a strict concept of one particle quantum states for gluons and quarks. We propose a non-perturbative approach based on Weyl symmetric solutions to fully nonlinear equations of motion, resulting in a full space of dynamical solutions classified by a finite set of integer numbers.