DISCUSSIONS ON THE TRANSITION BETWEEN E4 SOLUTIONS AND M4 SOLUTIONS IN ENERGY BAND THEORY

WANG MING-ZHONG; ZHENG XI-TE; WANG KE-LIN; XIAN DING-CHANG; ZHANG ZHENG-GANG

Chinese Physics C> 1982, Vol. 6> Issue(2) : 142-153

DISCUSSIONS ON THE TRANSITION BETWEEN E₄ SOLUTIONS AND M₄ SOLUTIONS IN ENERGY BAND THEORY

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Abstract：
The most probable escape path (MPEP) between vacuums, determined with WKBmethod, is expressed by different functions corresponding to the classical solutions offield equations in Euclidean space or in Minkowski Space while the potential U ishigher or lower than the energy E respectively. But the WKB method will not be validnearby the turning point u=E. In this paper we give the equations satisfied in thevicinity of turning point by MPEP which connects E₄ and M₄ solutions. The energylevels of physical θ vacuums obtained in terms of periodic potential in winding numberspace are not equal to the energy of original vacuums. The MPEP and also the poten-tial depend on positions of energy levels. Conversly, the energy levels are determined bypotential. We explain how to account this selfconsistently.

References

[1]

Khalil M. Bitar, Shau-Jin Chang, Phys. Rev., D17(1978), 486.[2] C. Callan, R. Daehen, D. Gross, Phys. Lett., 63B(1976), 334.[3] 王滋等,1980年广州拉子物理理论会议上的报告.0[4] Khalil M. Bitar, Bhau-Jin Chang, Phys. Rev., D18(1978), 435.[5] A. S. Dauydov,"Qnantum- Mechanics ", Pergamon Press.[6] 雷日克,格拉德斯坦,“函数表与积分表”.1959年高等教育出版社.[7] V. De Alfaro, B. Fubini, G. Furlan, Phys. Lett., 72B(1977), 203[8] 吴泳时,1978年广州规范场会议述评报告汇编.

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WANG MING-ZHONG, ZHENG XI-TE, WANG KE-LIN, XIAN DING-CHANG and ZHANG ZHENG-GANG. DISCUSSIONS ON THE TRANSITION BETWEEN E₄ SOLUTIONS AND M₄ SOLUTIONS IN ENERGY BAND THEORY[J]. Chinese Physics C, 1982, 6(2): 142-153.

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Received: 1983-03-03
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

DISCUSSIONS ON THE TRANSITION BETWEEN E₄ SOLUTIONS AND M₄ SOLUTIONS IN ENERGY BAND THEORY

Received Date: 1983-03-03
Accepted Date: 1900-01-01
Available Online: 1982-04-05

Abstract: The most probable escape path (MPEP) between vacuums, determined with WKBmethod, is expressed by different functions corresponding to the classical solutions offield equations in Euclidean space or in Minkowski Space while the potential U ishigher or lower than the energy E respectively. But the WKB method will not be validnearby the turning point u=E. In this paper we give the equations satisfied in thevicinity of turning point by MPEP which connects E₄ and M₄ solutions. The energylevels of physical θ vacuums obtained in terms of periodic potential in winding numberspace are not equal to the energy of original vacuums. The MPEP and also the poten-tial depend on positions of energy levels. Conversly, the energy levels are determined bypotential. We explain how to account this selfconsistently.