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Perturbation expansions in quantum field theory. (English) Zbl 1110.81143

Summary: A short history is given of the study of the problem of the divergence of perturbation expansions in quantum field theory from the initial work of C. A. Hurst [Proc. Camb. Philos. Soc. 48, 625–639 (1952; Zbl 0048.44701)], W. Thirring [Helv. Phys. Acta 26, 33–52 (1953; Zbl 0051.20906)] and A. Petermann [Helv. Phys. Acta 26, 291–299 (1953; Zbl 0053.47602)] up to string theory.

MSC:

81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory

Keywords:

divergence
Full Text: DOI

References:

[1] Petermann, A., Helv. Phys. Acta, 26, 291 (1953) · Zbl 0053.47602
[2] Le Guillou, J. C.; Zinn-Justin, J., Large order behaviour of perturbation theory, (Current Physics-Sources and Comments, Vol. 7 (1990), North Holland: North Holland Amsterdam) · Zbl 0978.82507
[3] Rivers, R. J., (Path Integral Methods in Quantum Field Theory (1987), Cambridge University Press) · Zbl 0648.46064
[4] Dyson, F. J., Phys. Rev., 85, 631 (1952) · Zbl 0046.21501
[5] Wightman, A., (Zichichi, A., The whys of subnuclear physics: Proceedings of the 1977 international school of subnuclear physics. The whys of subnuclear physics: Proceedings of the 1977 international school of subnuclear physics, Erice, Trapani, Sicily, July 23-August 10, 1977 (1979), Plenum Press: Plenum Press New York)
[6] Schweber, S. S., (QED and the Men Who Made it: Dyson, Feynman, Schwinger, and Tomonaga (1994), Princeton University Press: Princeton University Press New Jersey) · Zbl 0815.01011
[7] Bender, C. M., J. Math. Phys., 11, 797 (1976)
[8] Jaffe, A., Commun. Math. Phys., 1, 127 (1965) · Zbl 0127.19706
[9] Dimock, J., Commun. Math. Phys., 35, 347 (1974)
[10] Lipatov, L. N., Sov. Phys. JETP, 45, 216 (1977)
[11] Lautrup, B., Phys. Lett., B69, 109 (1977)
[12] Chadha, S.; Olesen, P., Phys. Lett., B72, 87 (1977)
[13] Heisenberg, W.; Euler, H., Z. Phys., 98, 714 (1936) · Zbl 0013.18503
[14] Schwinger, J., (Particles, Sources and Fields (1973), Addison-Wesley: Addison-Wesley Reading, Massachusetts) · Zbl 0155.32302
[15] Gross, D. J.; Periwal, V., Phys. Rev. Lett., 60, 2105 (1988)
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