GORDON DECOMPOSITIONS FOR γ-TYPE MATRICES AND SOME OF THEIR APPLICATIONS

SU Jun-Chen; WU Shi-Shu

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2024年10月30日

Chinese Physics C> 1987, Vol. 11> Issue(5) : 644-652

GORDON DECOMPOSITIONS FOR γ-TYPE MATRICES AND SOME OF THEIR APPLICATIONS

SU Jun-Chen ^, ,
WU Shi-Shu

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Abstract：
In this paper, some decomposotion formulas of γ-type matrices are derived based on Gordon identities. As an illustration of the application of these formulas, the one gluon exchange potential between quark and antiquark is rederived which appears to be different from that obtained by Faessler, et al. As another illustration, the correct reduction of the γ-matrices appearing in the kernel function of Bethe-Salpeter equation for quark-antiquark system is achieved and yields an expression different from that derived by Mitre whose calculation was grounded on a wrong decomposition formula for one γ-type matrix.

References

[1]

J. D. Bjorken S. D. Drell: Relativistic Quantum Mechanics, New York, McCraw-Hill, 1964.C. Itzykson J. B. Zuber: Quantum Field Theory. McGraw-Hill, 1980.[2] A. N. Mitra, Z. Phys., C8(1981), 25.[3] A. N. Mitra I. Santhanam, Z. Phys., C8(1981), 33.[4] A. N. Mitra D. S. Kulshreshtha, Phys. Rev., D26(1982), 3123.[5] A. De Rujula, et al. Phys. Rev., D12(1975), 147.[6] A. Faessler, et. al. Phys. Rev., D26(1982), 3280.[7] 苏君辰、王秀江、朱翅银, 高能物理与核物理, Vol. 10 (1986), 40.[8] M. Fierz, Phys., 104(1937), 553.K. M. Case, Phyr. Rev., 97(1955), 810.

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SU Jun-Chen and WU Shi-Shu. GORDON DECOMPOSITIONS FOR γ-TYPE MATRICES AND SOME OF THEIR APPLICATIONS[J]. Chinese Physics C, 1987, 11(5): 644-652.

SU Jun-Chen and WU Shi-Shu. GORDON DECOMPOSITIONS FOR γ-TYPE MATRICES AND SOME OF THEIR APPLICATIONS[J]. Chinese Physics C, 1987, 11(5): 644-652. 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

GORDON DECOMPOSITIONS FOR γ-TYPE MATRICES AND SOME OF THEIR APPLICATIONS

SU Jun-Chen ^,
WU Shi-Shu

Corresponding author: SU Jun-Chen,

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1987-10-05

Abstract: In this paper, some decomposotion formulas of γ-type matrices are derived based on Gordon identities. As an illustration of the application of these formulas, the one gluon exchange potential between quark and antiquark is rederived which appears to be different from that obtained by Faessler, et al. As another illustration, the correct reduction of the γ-matrices appearing in the kernel function of Bethe-Salpeter equation for quark-antiquark system is achieved and yields an expression different from that derived by Mitre whose calculation was grounded on a wrong decomposition formula for one γ-type matrix.