Geodesic
Behavior of massless feynman integrals near singular points
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 3, pp. 372-380 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved for some class of massless Feynman amplitudes including one-loop integrals that on the leading Landau surface these integrals can only have poles and logarithmic or square root-type singularities; the corresponding critical points (in the sense of the theory of singularities of differentiable mappings) are simple. Diagrams having nonisolated critical points are considered. The question of possible coincidence of leading Landau surfaces for the graph and its sub- or quotinent-graphs is studied. 
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     author = {A. I. Zaslavskii},
     title = {Behavior of~massless feynman integrals near singular points},
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}
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A. I. Zaslavskii. Behavior of massless feynman integrals near singular points. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 3, pp. 372-380. http://geodesic.mathdoc.fr/item/TMF_1989_80_3_a4/

[1] Zavyalov O. I., Perenormirovannye diagrammy Feinmana, Nauka, M., 1979 | MR

[2] Smirnov V. A., TMF, 44:3 (1980), 307–320 | MR

[3] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, T. 1, Mir, M., 1986 | MR

[4] Sato M., Miwa T., Jimbo M., Oshima T., Publ. RIMS., Suppl., 12 (1977), 387–439 | DOI | MR | Zbl

[5] Smirnov V. A., TMF, 46:2 (1981), 199–212 | MR

[6] Zaslavskii A. I., “Volnovye fronty feinmanovskikh integralov i golonomnye sistemy s regulyarnymi osobennostyami”, Kompleksnyi analiz i matematicheskaya fizika, Institut fiziki im. L. V. Kirenskogo SO AN SSSR, Krasnoyarsk, 1987, 36; Функц. анализ и его прилож., 22:3 (1988), 71–72 | MR

[7] Eden R., Landshoff P., Olive D., Polkinghorne J., The Analytic $S$-Matrix, Cambr. Univ. Press, Cambr., 1966 | MR | Zbl

[8] Fam F., Osobennosti protsessov mnogokratnogo rasseyaniya, Mir, M., 1972 | MR

[9] Fam F., Vvedenie v topologicheskoe issledovanie osobennostei Landau, Mir, M., 1970

[10] Kawai T., Stapp H. P., Publ. RIMS, Suppl., 12 (1977), 155–232 | DOI | MR | Zbl

[11] Kashiwara M., Kawai T., Ann. Math. Stud., 93, 1979, 123–137 | MR | Zbl

[12] Kawai T., Stapp H. P., Microlocal Analysis of Infrared Singularities, Preprint RIMS-598, RIMS, Kyoto, 1987 | MR

[13] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii, T. 1, Nauka, M., 1982 ; Т. 2, Наука, М., 1984 | MR

[14] Smirnov V. A., TMF, 46:1 (1981), 27–32 | MR

[15] Sato M., Kawai T., Kashiwara M., “Microfunctions and Pseudodifferential Equations”, Lect. Notes in Math., 287, Springer, Berlin, 1973, 265–529 | DOI | MR