A Rigorous Method for Calculating the Casimir Effect

NI Guang-Jiong; ZHANG Min; GONG Jia-Wen

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 1991, Vol. 15> Issue(8) : 695-700

A Rigorous Method for Calculating the Casimir Effect

Physics Department,Fudan University,Shanghai 200433

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Abstract：
Using the Plana summation formula in complex variable function theory,we have calculated the Casimir energy related to the zero-point fluctuations of electromagnetic fields in three dimensional space without introducing any cutoff parameter or function.The finite analytical expression obtained coincides precisely with the known experimental and theoretical results.The Casimir effects in high dimensional space and relevant to massive scalar field are also discussed.

References

[1]

H. B. G. Casimir, Proc. kQn. Med. Akad. Wet 51(1948), 793.[2] C. Iczykson and J-B Zubet, Quantum. Field Theory, (MCGRAW-HILL). p. 138[3] B. V. Deryagin and I. I. Abricosova, J. Exp. Theor. Phys. U. S. S. R. 21(1951) 945; M. J. Sparnaay,Phyrica, 24(1958), 751. D. Tabor and R. M. S. Winterton. Proc. Roy. Soc., A312(1969), 435.[4] G. Plunien, B. Miiller and W. Greiner, Phys. Rep., 134(1986), 87.[5] E. LindelSf, Le Calcul des Residues, (Gauthier-Villars, Paris, France, 1905) Chap. 11I.[6] L. H. Ford, Phys. Rev. D., 38(1988), 529.[7] Yu-Liang Liu and Guang-jiong Ni, .Phys. Rev., D38(1988), 3840.[8] I. S. Gradshteyn and 1. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, 1980), p.325, 1074.[9] H. Verschelde, L. Wine and P. Phariseau, Phys. Lett., 149B(1984), 396.

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NI Guang-Jiong, ZHANG Min and GONG Jia-Wen. A Rigorous Method for Calculating the Casimir Effect[J]. Chinese Physics C, 1991, 15(8): 695-700.

NI Guang-Jiong, ZHANG Min and GONG Jia-Wen. A Rigorous Method for Calculating the Casimir Effect[J]. Chinese Physics C, 1991, 15(8): 695-700. 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

A Rigorous Method for Calculating the Casimir Effect

Corresponding author: NI Guang-Jiong,

Physics Department,Fudan University,Shanghai 200433

Received Date: 1900-01-01
Accepted Date: 1900-01-01
Available Online: 1991-08-05

Abstract: Using the Plana summation formula in complex variable function theory,we have calculated the Casimir energy related to the zero-point fluctuations of electromagnetic fields in three dimensional space without introducing any cutoff parameter or function.The finite analytical expression obtained coincides precisely with the known experimental and theoretical results.The Casimir effects in high dimensional space and relevant to massive scalar field are also discussed.