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

SU Jun-Chen; WU Shi-Shu

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

Abstract
HTML
Reference
Related

PDF

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.

[1]	WANG Jian-Hua , LI Kang , Dulat Sayipjamal , . Klein-Gordon oscillators in noncommutative phase space. Chinese Physics C, 2008, 32(10): 803-806. doi: 10.1088/1674-1137/32/10/007
[2]	ZHANG Ai-Ping , QIANG Wen-Chao . Exact Bound Solution of the Klein-Gordon Equation and the Dirac Equation with Rosen-MorseⅡ Potential. Chinese Physics C, 2007, 31(11): 1027-1031.
[3]	. A Possible Relation between the Neutrino Mass Matrix and the Neutrino Mapping Matrix. Chinese Physics C, 2006, 30(7): 591-598.
[4]	DAI Lian-Rong , PAN Feng . Analytical Expressions for Reduced Coefficients of S_fS_f－1. Chinese Physics C, 2003, 27(3): 238-244.
[5]	YAN Jun , TAO Bi-You . A Electric Sine-Gordon Soliton Solution in Two-Dimensional Dilaton Gravity Model. Chinese Physics C, 2003, 27(9): 767-769.
[6]	Medina Ablikim , Edward Corrigan . Boundary Reflection Factor of the Supersymmetric Sinh-Gordon Model. Chinese Physics C, 2002, 26(S1): 47-53.
[7]	Sa Benhao , Tai An . Reduction of Strangeness Suppression and Strange Antibaryon Production in Sulphur-Nucleus Collisions at 200A GeV. Chinese Physics C, 1998, 22(1): 41-47.
[8]	Tai An , Sa Benhao . Reduction of Strange Quark Suppression in Relativistic Nucleus-Nucleus Collisions. Chinese Physics C, 1998, 22(5): 434-439.
[9]	Shi Kangjie , Yang Wenli , Fan Heng , Hou Boyu . Bosonized Vertex Operators Realize Z-F Algebra for Z_n Symmetric Belavin R Matrix. Chinese Physics C, 1997, 21(8): 706-713.
[10]	Chen Min , Hou Boyu , Shi Kangjie . Reflection Matrix of Zⁿ Belavin Model. Chinese Physics C, 1996, 20(9): 794-800.
[11]	Zou Pengcheng , Huang Yongchang . Proof of. Chinese Physics C, 1995, 19(9): 796-799.
[12]	Zhao Liu . Hamiltonian Reductions of Supersymmetric Self-Dual Yang-Mills Fields. Chinese Physics C, 1994, 18(2): 119-126.
[13]	HOU Bo-Yu , ZHAO Liu . Conformally Reduced WZNW Theory,New Extended Chiral Algebras and Their Associated Toda Type Integrable Systems (Ⅰ) General Framework. Chinese Physics C, 1993, 17(1): 28-37.
[14]	HOU Bo-Yu , ZHAO Liu . Conformally Reduced WZNW Theory,New Extended Chiral Algebras and Their Associated Toda Type Integrable Systems (Ⅱ)An Example. Chinese Physics C, 1993, 17(3): 241-251.
[15]	HU Zhan-Ning , HOU Bo-Yu . Factorizable S-Matrix and Symmetry Operator With Toroidal Rapidity Values. Chinese Physics C, 1992, 16(11): 978-990.
[16]	ZHU Dong-Pei . Eigenmatrices of Dual Transformation and Its Application. Chinese Physics C, 1991, 15(1): 38-41.
[17]	HOU Bo-Yu , LI Wei . VIRASORO ALGEBRA FOR THE THEORY OF THE REDUCED GRAVITY. Chinese Physics C, 1987, 11(1): 137-141.
[18]	DAI An-Ying . LEVINSON'S THEOREM FOR KLEIN-GORDON EQUATIONS WITH POTENTIAL TAILS. Chinese Physics C, 1987, 11(5): 620-628.
[19]	HUANG Nian-Ning . ON THE ONE-SOLITON SOLUTIONS OT SUPER-GORDON EGUATION. Chinese Physics C, 1985, 9(3): 382-384.
[20]	WU Yong-Shi , GE Mo-Lin . THE GEOMETRIC MEANING OF THE RICCATI EQUATION RELATED TO SINE-GORDON EQUATION. Chinese Physics C, 1983, 7(5): 560-564.

Access

Get Citation

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

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(2163)
PDF Downloads(391)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
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.