Geodesic
Representations for three-body $T$-matrix on unphysical sheets. I
Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 3, pp. 450-477 Cet article a éte moissonné depuis la source Math-Net.Ru

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Explicit representations are formulated for the Faddeev components of three-body $T$-matrix continued analytically on unphysical sheets of the energy Riemann surface. According to the representations, the $T$-matrix is obviously expressed in terms of its components taken on the physical sheet only. The representations for $T$-matrix are used to construct similar representations for analytical continuation of three-body scattering matrices and resolvent. Domains on unphysical sheets are described where the representations obtained can be applied. 
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A. K. Motovilov. Representations for three-body $T$-matrix on unphysical sheets. I. Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 3, pp. 450-477. http://geodesic.mathdoc.fr/item/TMF_1996_107_3_a8/

[1] G. Gamow, Z. Phys., 51 (1928), 204–212 | DOI | Zbl

[2] R. Jost, Helv. Phys. Acta, 20 (1947), 250–266 | MR

[3] R. Nyuton, Teoriya rasseyaniya voln i chastits, Mir, M., 1969 | MR

[4] V. de Alfaro, T. Redzhe, Potentsialnoe rasseyanie, Mir, M., 1986

[5] G. Parravicini, V. Gorini, E. C. G. Sudarshan, J. Math. Phys., 21 (1980), 2208–2226 | DOI | MR | Zbl

[6] A. Böhm, J. Math. Phys., 22 (1981), 2813–2823 | DOI | MR

[7] A. Boum, Kvantovaya mekhanika: osnovy i prilozheniya, Mir, M., 1990

[8] J. Schwinger, Ann. Phys., 9 (1960), 169–193 | DOI | MR | Zbl

[9] A. Grossmann, J. Math. Phys., 5 (1964), 1025–1037 | DOI | MR | Zbl

[10] E. Balslev, J. M. Combes, Commun. Math. Phys., 22 (1971), 280–294 | DOI | MR | Zbl

[11] J. S. Howland, J. Math. Anal. Appl., 50 (1975), 415–437 | DOI | MR | Zbl

[12] J. Rauch, J. Funct. Anal., 35 (1980), 304–315 | DOI | MR | Zbl

[13] L. P. Horwitz, E. Katznelson, J. Math. Phys., 24 (1983), 848–859 | DOI | MR | Zbl

[14] E. Balslev, E. Skibsted, Ann. Inst. H.Poincaré, 43 (1985), 369–397 | MR | Zbl

[15] E. Brandas, N. Elander (eds.), Resonances, Springer-Verlag, 1987 | MR

[16] W. Hunziker, Commun. Math. Phys., 132 (1990), 177–188 | DOI | MR | Zbl

[17] S. Albeverio, F. Gestezi, R. Kheeg-Kron, Kh. Kholden, Reshaemye modeli v kvantovoi mekhanike, Mir, M., 1991 | MR

[18] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, T. I–IV, Mir, M., 1977–1982 | MR

[19] P. Laks, R. Fillips, Teoriya rasseyaniya, Mir, M., 1971 ; Теория рассеяния для автоморфных функций, Мир, М., 1977 | MR

[20] B. S. Pavlov, S. I. Fedorov, Algebra i analiz, 1:2 (1989), 132–169

[21] S. I. Fedorov, Matem. sb., 181:6 (1990), 833–864 | MR | Zbl

[22] A. K. Motovilov, TMF, 98:2 (1994), 248–265 | MR | Zbl

[23] C.-Y. Hu, A. K. Bhatia, Muon Catalyzed Fusion, Vol. 5/6, 1990/91, 439–444

[24] L. D. Faddeev, Tr. MIAN SSSR, 69, 1963, 1–125 | MR

[25] J. Ginibre, M. Moulin, Ann. Inst. H. Poincaré, Sect. A, 21 (1974), 97–145 | MR

[26] D. R. Yafaev, Matem. sb., 106 (1978), 622–640 | MR | Zbl

[27] D. R. Yafaev, TMF, 37:1 (1978), 48–57 | MR

[28] S. P. Merkurev, Teoriya rasseyaniya dlya sistemy trekh chastits v konfiguratsionnom prostranstve, Diss. na soisk. uch. st. d.f.-m.n., LGU, L., 1978

[29] S. P. Merkurev, L. D. Faddeev, Teoriya rasseyaniya dlya sistem neskolkikh chastits, Nauka, M., 1985 | MR

[30] V. Enss, Lecture Notes in Math., 1159, 1985, 39–176 | DOI | MR | Zbl

[31] J. Derezinski, Ann. Math., 138 (1993), 427–476 | DOI | MR | Zbl

[32] A. A. Kvitsinskii, Yu. A. Kuperin, S. P. Merkurev, A. K. Motovilov, S. L. Yakovlev, EChAYa, 17:2 (1986), 267–317 | MR

[33] Yu. A. Kuperin, K. A. Makarov, S. P. Merkuriev, A. K. Motovilov, B. S. Pavlov, J. Math. Phys., 31 (1990), 1681–1690 | DOI | MR | Zbl

[34] E. Shmid, Kh. Tsigelman, Problema trekh tel v kvantovoi mekhanike, Nauka, M., 1979 | MR | Zbl

[35] V. B. Belyaev, Lektsii po teorii malochastichnykh sistem, Energoatomizdat, M., 1986

[36] K. Meller, Yu. V. Orlov, EChAYa, 20 (1989), 1341–1395

[37] J. J. Derezinski, Math. Phys., 28 (1987), 1080–1088 | DOI | MR | Zbl

[38] Yu. V. Orlov, V. V. Turovtsev, ZhETF, 86:5 (1984), 1600–1617 | MR

[39] A. K. Motovilov, TMF, 95:3 (1993), 427–438 | MR | Zbl

[40] A. K. Motovilov, YaF, 56:7 (1993), 61–65 | MR

[41] A. K. Motovilov, Proc. of 14th Intern. Conf. on Few Body Problems in Physics (Williamsburg, USA, May 26–31 1994), 816–819

[42] I. M. Gelfand, G. E. Shilov, Prostranstva osnovnykh i obobschennykh funktsii, T. 1, Fizmatgiz, M., 1958 | MR | Zbl