Abstract
We show that the series expansion of quantum field theory in Feynman diagrams can be explicitly mapped on the partition function of simplicial string theory—the theory describing embeddings of two-dimensional (2D) simplicial complexes into the spacetime of the field theory. The summation over 2D geometries in this theory is obtained from the summation over the Feynman diagrams and the integration over the Schwinger parameters of the propagators. We discuss the meaning of the obtained relation and derive the one-dimensional analog of the simplicial theory using the example of a free relativistic particle.
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References
A. M. Polyakov, Gauge Fields and Strings (Harwood Academic, Chur, Switzerland, 1987).
J. M. Maldacena, Adv. Theor. Math. Phys. 2, 231 (1998) [Int. J. Theor. Phys. 38, 1113 (1999)]; hep-th/9711200; S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett. B 428, 105 (1998); hep-th/9802109; E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998).
E. T. Akhmedov, Usp. Fiz. Nauk 171, 1005 (2001) [Phys. Usp. 44, 955 (2001)]; hep-th/9911095.
R. Gopakumar, hep-th/0308184; hep-th/0402063.
C. S. Lam and J. P. Lebrun, Nuovo Cimento A 4, 397 (1969); See as well N. N. Bogolyubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, 3rd ed. (Nauka, Moscow, 1973; Wiley, New York, 1980).
J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965; Nauka, Moscow, 1978).
J. t’Hooft, Nucl. Phys. B 72, 461 (1974).
A. Alexandrov, A. Mironov, and A. Morozov, hepth/0310113.
C. Kristjansen, J. Plefka, G. W. Semenoff, and M. Staudacher, Nucl. Phys. B 643, 3 (2002); hep-th/0205033.
T. L. Ivanenko and M. I. Polikarpov, Nucl. Phys. (Proc. Suppl.) 26, 536 (1992); M. N. Chernodub and M. I. Polikarpov, hep-th/9710205.
A. P. Isaev, Nucl. Phys. B 662, 461 (2003); hepth/0303056.
E. T. Akhmedov and V. V. Dolotin (in press).
F. David, hep-th/9303127; J. Ambjorn, M. Carfora, and A. Marzuoli, hep-th/9612069; H. W. Hamber and R. M. Wiliams, hep-th/9607153.
E. T. Akhmedov, Phys. Lett. B 442, 152 (1998); hep-th/9806217; hep-th/0202055.
J. D. Bjorken, Doctoral Thesis (Stanford, 1958).
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From Pis’ma v Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}\) Fiziki, Vol. 80, No. 4, 2004, pp. 247–254.
Original English Text Copyright © 2004 by Akhmedov.
This article was submitted by the author in English.
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Akhmedov, E.T. Expansion in Feynman graphs as simplicial string theory. Jetp Lett. 80, 218–225 (2004). https://doi.org/10.1134/1.1813675
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DOI: https://doi.org/10.1134/1.1813675