Investigations of Infrared Divergence in Quantum Field Theory from Unitarities and Analyticities

PENG Hong-An

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1992, Vol. 16> Issue(10) : 891-899

Investigations of Infrared Divergence in Quantum Field Theory from Unitarities and Analyticities

PENG Hong-An ^,

Department of Physics,Peking University,100871

Abstract
HTML
Reference
Related

PDF

Abstract：
In this paper we have investigated the infrared divergence in QFT from the point of view of unitarities and analyticities.We have shown that in QED,the infrared divergence for the imaginary part of a bubble diagram at any order of a would be canceled each other between the set of cutting-bubble diagrams got from cutting rules of Landau Cutkosky.From the concept of generalized optical theorem and the hypothesis of analyticities of the scattering amplitude,we have drawn the physical connotation from the general formula of unitarity.for "forward scattering processes",and thus getting a criterion in QED for whether in a process there exist infrared divergence or not.Also from the variation of thresholds of a bubble diagram of π(q²)in the -q² plane as the photon mass λ approaches to zero,we have shown diagrammatically how the infrared divergence in the corresponding cutting-bubble diagrams be canceled between them.At last we give a short discussion about difficulties and problems for treating infrared divergence in QCD.

References

[1]

D. R. Yennie, S. R. Frautschi and H. Surra, inn. of Phys., 13(1961), 379.[2] J. Cornwall and G. Tiktopoulos, Phys. Rev., D13(1976), 3370; Y. P. Yao, Phys. Rev. Lett., 36(1976), 542; A. Sugamoto, Phys. Rev., D15 (1977), 1065.[3] 吴泳时、戴元本，Scientio Sinico, 19 (1976), 65, J. Cornwall and G. Tiktopoulos, Phys. Rev., D13(1976), 3370.[4] 戴元本，相互作用的规范理论，科学出版社，1987.[5] 彭宏安，北京大学学报(自然科学版)，No. 5 1984, 36.[6] L. D. Landau, Nucl. Phys., 13 (1959), 181. R. E. Cutkosky, J. Math. Phy., 1 (1960), 424,[7] A. H. Mueller, Phys. Rev., D2 (1970), 2963; D4 (1971), 150, P. D. B. Collins, "An introductionto Regge theory and high energy physics", Cambridge Univ. Press, 1977.[8] J. Frenkel, M-L. Frenkel and J. C. Taylor, Nucl. Phys., B124 (1977), 268.

[1]	LIAO Yi . Field Theory on Non-commutative Space-Time and Some Related Phenomenology. Chinese Physics C, 2007, 31(9): 860-863.
[2]	XING Zhi-Zhong , ZHOU Shun . Why is the 3×3 Neutrino Mixing Matrix Almost Unitary in Realistic Seesaw Models?. Chinese Physics C, 2006, 30(9): 828-832.
[3]	ZHAO Xiu-Mei , CAO Li-Ke , YANG Tao , YUE Rui-Hong . Integrability of a Quantum Derivative Nonlinear Schrodinger Model for Spin-1/2 Particle. Chinese Physics C, 2004, 28(9): 936-940.
[4]	WAN Ling-De , CAO Jun-Jie . Infrared Divergence in Loop Functions. Chinese Physics C, 2003, 27(5): 381-385.
[5]	JIANG Jin-Huan , LI Ai-Min , LI Zi-Ping . Quantum Field Theory of Optical Soliton Constrained Systems. Chinese Physics C, 2003, 27(6): 489-492.
[6]	DU Dong-Sheng . Infrared Divergence and Twist-3 Wave Functions in QCD Factorization for B→PP Decays. Chinese Physics C, 2002, 26(S1): 11-15.
[7]	LONG ZhengWen , Li ZiPing . Global Symmetry and Quantal Conservation Laws for a Gauge-Invariant System With a Higher-Order Lagrangian. Chinese Physics C, 2000, 24(2): 106-112.
[8]	ZHANG PengFei , RUAN TuNan . Spin Operators in the Quantum Field Theory. Chinese Physics C, 2000, 24(8): 775-779.
[9]	Liu Chuan . Infra-red Renormalization Group Calculation of the O(N) Model in the Broken Phase. Chinese Physics C, 1999, 23(6): 594-600.
[10]	Jia Huanyu , Wang Shunjin , Tan Youheng . Possibility of Hubble Constant and Background Infrared Radiation Measurements With Yangbajing RPC Carpet Experiment. Chinese Physics C, 1999, 23(3): 217-222.
[11]	Chen Xiangjun , Zhang Weining , Wang Wei . Infrared Divergences of Three-loop Vacuum Graghs of Quark Field at Hight Temperature. Chinese Physics C, 1999, 23(3): 260-267.
[12]	Chen Xiangjun , Liu Lianshou . Infrared Divergences of Three-Loop Vacuum Graghs of Gluon Field at Finite Temperature. Chinese Physics C, 1998, 22(2): 133-140.
[13]	Chen Xiangjun , Liu Lianshou . Regularization of Infrared Divergences in the Vacuum Graphs of Massless Field at Finite Temperature. Chinese Physics C, 1997, 21(5): 425-432.
[14]	Gao Xiaochun , Gao Jun , Fu Jian . Invariant-Related Unitary Transformation Method and Evolution of the Third-Quantized Wave Function of the Universe. Chinese Physics C, 1996, 20(3): 226-233.
[15]	Chen Xiangjun , Liu Lianshou . Regularization of Angular Infrared Divergence of Massless Theory at Finite Temperature. Chinese Physics C, 1995, 19(10): 907-910.
[16]	PAN Feng . ANALYTICAL EXPRESSIONS OF SOME MULTIPLICITY-FREE ISOSCALAR FACTORS FOR SU_N SO_N UNDER THE ORTHOGONAL BASIS. Chinese Physics C, 1990, 14(9): 851-854.
[17]	MA Bo-Qiang , SUN Ji . THE EMC EFFECT AND THE LIGHT-CONE QUANTUM FIELD THEORY. Chinese Physics C, 1990, 14(8): 684-691.
[18]	DONG Shao-Jing . NORMAL FUZZY LATTICE ——A PROBABLE FERMIONIC ACTION WITHOUT MULTIPLICITY BUT REMAINS CONVARIANT AND CHIRAL LIMIT. Chinese Physics C, 1987, 11(4): 543-548.
[19]	RUAN TU-NAN , HE ZUO-XIU , HUANG TAO . ON THE CONJUGATE FIELD QUANTITY AND THE DEFINITION OF THE RELATIVISTIC WAVE FUNCTION IN THE COMPOSITE FIELD THEORY. Chinese Physics C, 1979, 3(3): 272-276.
[20]	CHANG CHAO-SHIE , HO TSU-HSIU . THE PERTURBATION EXPANSION OF THE QUANTIZED COMPOSITE FIELD THEORY AND GAUGE INVARIANCE. Chinese Physics C, 1978, 2(2): 119-130.

Access

Get Citation

PENG Hong-An. Investigations of Infrared Divergence in Quantum Field Theory from Unitarities and Analyticities[J]. Chinese Physics C, 1992, 16(10): 891-899.

PENG Hong-An. Investigations of Infrared Divergence in Quantum Field Theory from Unitarities and Analyticities[J]. Chinese Physics C, 1992, 16(10): 891-899. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

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

Article Metric

Article Views(2734)
PDF Downloads(474)
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

Investigations of Infrared Divergence in Quantum Field Theory from Unitarities and Analyticities

PENG Hong-An ^,

Corresponding author: PENG Hong-An,

Department of Physics,Peking University,100871

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1992-10-05

Abstract: In this paper we have investigated the infrared divergence in QFT from the point of view of unitarities and analyticities.We have shown that in QED,the infrared divergence for the imaginary part of a bubble diagram at any order of a would be canceled each other between the set of cutting-bubble diagrams got from cutting rules of Landau Cutkosky.From the concept of generalized optical theorem and the hypothesis of analyticities of the scattering amplitude,we have drawn the physical connotation from the general formula of unitarity.for "forward scattering processes",and thus getting a criterion in QED for whether in a process there exist infrared divergence or not.Also from the variation of thresholds of a bubble diagram of π(q²)in the -q² plane as the photon mass λ approaches to zero,we have shown diagrammatically how the infrared divergence in the corresponding cutting-bubble diagrams be canceled between them.At last we give a short discussion about difficulties and problems for treating infrared divergence in QCD.