Geodesic
Riemann Surfaces of Some Static Dispersion Models and Projective Spaces
Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 3, pp. 414-425 
V. A. Meshcheryakov; D. V. Meshcheryakov. Riemann Surfaces of Some Static Dispersion Models and Projective Spaces. Teoretičeskaâ i matematičeskaâ fizika, Tome 130 (2002) no. 3, pp. 414-425. http://geodesic.mathdoc.fr/item/TMF_2002_130_3_a2/
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     author = {V. A. Meshcheryakov and D. V. Meshcheryakov},
     title = {Riemann {Surfaces} of {Some} {Static} {Dispersion} {Models} and {Projective} {Spaces}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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We show that the analytic continuation of the $S$-matrix elements, which are meromorphic functions of the energy $\omega $ in the complex plane with the cuts $(-\infty ,-1]$, $[+1,+\infty )$, from the physical sheet to nonphysical ones results in a system of nonlinear difference equations. A global analysis of this system is performed in the projective spaces $P_{N}$ and $P_{N+1}$. We discuss the connection between the spaces $P_{N}$ and $P_{N+1}$ and obtain some particular solutions of the initial system.

[1] A. L. Machovariani, A. G. Rysetsky, Nucl. Phys. A, 515 (1990), 621 | DOI

[2] R. Oehme, Phys. Rev. D, 42 (1990), 4209 ; Phys. Lett. B, 252 (1990), 14 ; J. Mod. Phys. A, 10 (1995), 1995 | DOI | MR | DOI | DOI

[3] G. F. Chew, F. E. Low, Phys. Rev., 101 (1956), 1570 | DOI | MR | Zbl

[4] V. A. Mescheryakov, Statisticheskie modeli v diskretnom podkhode, Preprint No R-2369, OIYaI, Dubna, 1965; В. И. Журавлев, В. А. Мещеряков, ЭЧАЯ, 5 (1974), 173

[5] G. Wanders, Nuovo Cimento, 23 (1962), 816 ; В. А. Мещеряков, ЖЭТФ, 51 (1966), 648 | DOI | MR

[6] V. A. Meshcheryakov, Solutions of nonlinear problems of dispersion relations in projective spaces. Proc. of Symp. in Ahrenshoop, Preprint PHE81-7, Institut fur Hoohenenergiephysik Akademie der Wisserschaften der DDR, Zeuthen, 1981, p. 44

[7] V. I. Zhuravlev, V. A. Mescheryakov, K. V. Rerikh, YaF, 10 (1969), 168 | MR

[8] V. A. Mescheryakov, DAN SSSR, 174 (1967), 1054

[9] M. Froissart, R. Omnes, Compt. Rend. Acad. Sci., 245 (1957), 2203 | MR | Zbl