WEAK COUPLING APPROXIMATE SCHWINGER-DYSON EQUATION OF THE STRATON'S PROPAGATOR IN QUANTUM CHROMODYNAMICS AND ITS SOLUTIONS

Zhou Xian-jian; Xue Pei-you

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1980, Vol. 4> Issue(1) : 49-62

WEAK COUPLING APPROXIMATE SCHWINGER-DYSON EQUATION OF THE STRATON'S PROPAGATOR IN QUANTUM CHROMODYNAMICS AND ITS SOLUTIONS

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Abstract：
The weak coupling approximate Schwinger-Dyson equation of the straton's pro-pagator in 4-dimensional QCD theory and the problem of the straton's confinement are discussed. It is proved that, when we choose Landaugauge, the obtained Sch-winger-Dyson integral equation of the straton's propagator can be transformed into a very simple form. Then we change it into a first order non-linear differential equation. It has two solutions: a confining solution and a solution that has no con-finement for the stratons. The effective potential in QCD is derived by functional method, and the ground-state energy difference between these two solutions is discussed. In our approximation, we calculate the vacuum graph to the 2-loop diagrams, We may conclude that stratons are not confined in our approximation.

References

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t'Hooft, Nucl. Phys., B72 (1974), 461;B75 (1974), 461.[2] t'Hooft, C. G. Callen and D, J. Gross, Phys. Rev., D13 (1976), 1649.[3] 黄涛、薛丕友, 高能物理与核物理,3(1979), 188,[4] J. D. Bjorken and S. D. Drell, Relativiatic Quantum Fields, 290, McGraw-Hill Book Com-pant, 1965.[5] E. J. Eichten and F. L. Feinberg, Phys. Rev., D10 (1974), 3254.[6] 邝宇平, 动力学自发破缺, 广州会议评述报告, (1978).[7] R. Fukuda and T, Kugo, Nucl. Phys., B117 (1976), 250.[8] Predrag Cvitanoć, Phys. Rev., D14 (1976).1536.[9] R. Jaekiw, Phys. Rev., D9 (1974), 1686.[10] R.Fukuda and T. Kugo, Phys. Rev., D13 (1976), 3469.[11] J. M. Cormwall, R. Jackiw and E. Tomboulis, Phys. Rev., D10 (1974), 2428.

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Zhou Xian-jian and Xue Pei-you. WEAK COUPLING APPROXIMATE SCHWINGER-DYSON EQUATION OF THE STRATON'S PROPAGATOR IN QUANTUM CHROMODYNAMICS AND ITS SOLUTIONS[J]. Chinese Physics C, 1980, 4(1): 49-62.

Zhou Xian-jian and Xue Pei-you. WEAK COUPLING APPROXIMATE SCHWINGER-DYSON EQUATION OF THE STRATON'S PROPAGATOR IN QUANTUM CHROMODYNAMICS AND ITS SOLUTIONS[J]. Chinese Physics C, 1980, 4(1): 49-62. shu

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Received: 1978-11-11
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

WEAK COUPLING APPROXIMATE SCHWINGER-DYSON EQUATION OF THE STRATON'S PROPAGATOR IN QUANTUM CHROMODYNAMICS AND ITS SOLUTIONS

Zhou Xian-jian
Xue Pei-you

Received Date: 1978-11-11
Accepted Date: 1900-01-01
Available Online: 1980-02-05

Abstract: The weak coupling approximate Schwinger-Dyson equation of the straton's pro-pagator in 4-dimensional QCD theory and the problem of the straton's confinement are discussed. It is proved that, when we choose Landaugauge, the obtained Sch-winger-Dyson integral equation of the straton's propagator can be transformed into a very simple form. Then we change it into a first order non-linear differential equation. It has two solutions: a confining solution and a solution that has no con-finement for the stratons. The effective potential in QCD is derived by functional method, and the ground-state energy difference between these two solutions is discussed. In our approximation, we calculate the vacuum graph to the 2-loop diagrams, We may conclude that stratons are not confined in our approximation.