Topological properties of Landau curves in connection with Mandelstam's conjecture
Teoretičeskaâ i matematičeskaâ fizika, Tome 23 (1975) no. 3, pp. 335-347 Cet article a éte moissonné depuis la source Math-Net.Ru

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Feynman amplitude $F_G$ assotiated with the Feynman graph $G$ is considered for the case of the scalar scattering reaction of the $1+2\to 3+4$ type. Sufficient conditions of validity of the Mandelstam hypothesis [1] are found as conditions on the Landau curves $\mathscr L_G$ for the amplitude $F_G$, $G\in \Re$ where $\Re$ is a certain class of the Feynmann graphs introduced in the work. Application of the criteria obtained to the ladder graph is considered.
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     title = {Topological properties of {Landau} curves in connection with {Mandelstam's} conjecture},
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V. Z. Ènol'skii. Topological properties of Landau curves in connection with Mandelstam's conjecture. Teoretičeskaâ i matematičeskaâ fizika, Tome 23 (1975) no. 3, pp. 335-347. http://geodesic.mathdoc.fr/item/TMF_1975_23_3_a5/

[1] S. Mandelstam, Phys. Rev., 112 (1958), 1344 | DOI | MR

[2] V. S. Vladimirov, Ukr. matem. zh., 12 (1960), 132

[3] C. Risk, J. Math. Phys., 9 (1968), 2168 | DOI

[4] D. Ya. Petrina, Ukr. matem. zh., 16 (1964), 31 | MR | Zbl

[5] D. Ya. Petrina, ZhETF, 47 (1964), 524

[6] S. Coleman, R. Norton, Nuovo Cim., 38 (1965), 438 | DOI

[7] E. R. Speer, M. J. Westwater, Ann. Inst. H. Poincare, 14A (1971), 1 | MR | Zbl

[8] A. A. Logunov, I. T. Todorov, N. A. Chernikov, ZhETF, 42 (1962), 1285 ; И. Т. Тодоров, Аналитические свойства диаграмм Фейнмана квантовой теории поля, София, 1966 | MR | Zbl

[9] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Gostekhizdat, 1957 | MR

[10] D. Fotiadi, M. Froissart, J. Lascoux, F. Pham, Topology, 4 (1965), 159 ; J. Lascoux, Battele Rencontres, 1967, Lectures in Mathematics and Physics, W. A. Benjamin, N.-Y., 1968 | DOI | MR | Zbl | MR

[11] L. D. Landau, ZhETF, 37 (1959), 62 | Zbl

[12] R. Eden, P. Landshoff, D. Olive, The Analitic $S$-Matrix, Cambridge University Press, 1966 | MR | Zbl

[13] N. Nakanishi, Progr. Theor. Phys. (Kyoto), 22 (1959), 128 | DOI | MR | Zbl

[14] V. S. Vladimirov, Metody teorii funktsii mnogikh kompleksnykh peremennykh, «Nauka», 1964 | MR

[15] T. Regge, G. Barucchi, Nuovo Cim., 34:6 (1964), 106 | DOI | MR

[16] I. R. Shafarevich, Osnovy algebraicheskoi geometrii, «Nauka», 1972 | MR | Zbl

[17] R. E. Eden, Phys. Rev., 119 (1960), 1763 | DOI | MR