Inherent color symmetry of quantum Yang-Mills theory
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2020
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| author | Pak, Dmitriy G. Cai, Rong-Gen Tsukioka, Takuya Zhang, Pengming Zhou, Yu-Feng |
| author_facet | Pak, Dmitriy G. Cai, Rong-Gen Tsukioka, Takuya Zhang, Pengming Zhou, Yu-Feng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2009_13938 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Inherent color symmetry of quantum Yang-Mills theory Pak, Dmitriy G. Cai, Rong-Gen Tsukioka, Takuya Zhang, Pengming Zhou, Yu-Feng High Energy Physics - 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. |
| title | Inherent color symmetry of quantum Yang-Mills theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2009.13938 |