THE HERMITICITY OF RELATIVISTIC EQUAL-TIME EQUATION

WEI Hua; YIN Hong-Jun; RUAN Tu-Nan

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2024年10月30日

Chinese Physics C> 1985, Vol. 9> Issue(6) : 687-696

THE HERMITICITY OF RELATIVISTIC EQUAL-TIME EQUATION

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Abstract：
The differences of physical properties between several time-displacement operators are analyzed systematically. By using the Feynman propagator, a new time-displacement operator is reasonably constructed, with which the Hermite potential of relativistic equaltime equation is derived. Consequently, this equation is turned into a relativistic Schrödinger equation, in which the Hamiltonian is a Hermitian differentio-integral operator. Furthermore, the equaltime potential of minimum electro-magnetic coupling in first order is calculated. When the mass ratio of one particle to the other tends to infinity, the equation reduces to Dirac equation naturally.

References

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Nakanishi, N, Suppl. Prog. Theor. Phys, 43(1969), 1.[2] Hayashi, C., Munakata, Y., Prog. Theor. Phys.,7(1952), 481. Salpeter, E. E., Phys. Rev., 87(1952) ,328.[3] Dirac, P. A. M., Fock, V. A., Podolsky, B, Phys. Zeitz. Sowj., 2(1932), 468.[4] 阮图南, 朱熙泉, 何柞麻, 庆承端, 赵维勤, 高能物理与核物理, 5(1981), 393, 537.[5] 阮图南, 何柞麻, 黄涛, 高能物理与核物理, 3(1979), 272.[6] 卢里, D. ,粒子和场, 科学出版社, 1981, p. 386-393.[7] Feynman, R. P., Phys. Rev., 76(1949 ) , 749,769.[8] Schwinger, J., Phys. Rev., 74 (1948), 3.439.[9] Ruan Tu-nan, Ho Tso-hsiu, Proceedings of the 1980 Guangzhou Conference on Theoretical Particle Physics. p. 362[10] 卫华, 阮图南, 西北大学学报, 自然科学版, 1984, 待发表.

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WEI Hua, YIN Hong-Jun and RUAN Tu-Nan. THE HERMITICITY OF RELATIVISTIC EQUAL-TIME EQUATION[J]. Chinese Physics C, 1985, 9(6): 687-696.

WEI Hua, YIN Hong-Jun and RUAN Tu-Nan. THE HERMITICITY OF RELATIVISTIC EQUAL-TIME EQUATION[J]. Chinese Physics C, 1985, 9(6): 687-696. shu

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Received: 1900-01-01
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

THE HERMITICITY OF RELATIVISTIC EQUAL-TIME EQUATION

Corresponding author: WEI Hua,

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1985-12-05

Abstract: The differences of physical properties between several time-displacement operators are analyzed systematically. By using the Feynman propagator, a new time-displacement operator is reasonably constructed, with which the Hermite potential of relativistic equaltime equation is derived. Consequently, this equation is turned into a relativistic Schrödinger equation, in which the Hamiltonian is a Hermitian differentio-integral operator. Furthermore, the equaltime potential of minimum electro-magnetic coupling in first order is calculated. When the mass ratio of one particle to the other tends to infinity, the equation reduces to Dirac equation naturally.