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

PENG Hong-An

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《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

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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

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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.

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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

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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

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.