Abstract
We define the notion of C (2) N+1Ruijsenaars–Schneider models and construct their Lax formulation. They are obtained by a particular folding of the A 2N+1 systems. Their commuting Hamiltonians are linear combinations of Koornwinder–van Diejen ‘external fields’ Ruijsenaars–Schneider models, for specific values of the exponential one-body couplings but with the most general two double-poles structure as opposed to the formerly studied BC N case. Extensions to the elliptic potentials are briefly discussed.
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References
Ruijsenaars, S. N. M. and Schneider, H.: Ann. Phys. 170 (1986), 370.
Ruijsenaars, S. N. M.: Comm. Math. Phys. 110 (1987), 191.
J. F. Van Diejen and L. Vinet (eds), Calogero-Moser-Sutherland Models, CRM Ser. Math. Phys., Springer, New York, 2000, see in, particular contributions by H. Awata, K. Hasegawa, and V. I. Inozemtsev.
Van Diejen, J. F.: Compositio Math. 95 (1995), 183; In: D. Levi, L. Vinet and P. Winternitz (eds), Proc. Workshop on Integrability of Difference Equations, (Esterel Canada 1994), q-alg 9504012; J. Phys. A, 28 (1995), 369.
Van Diejen, J. F.: J. Math. Phys. 35 (1994), 2983.
Koornwinder, T. H. R.: Contemp. Math. 138 (1992), 189.
Komori, Y.: J. Phys. A, 30 (1997), 4341; Hikami, K. and Komori, Y.: Europhys. J. B, 5 (1998), 583; Komori, Y.: J. Math. Phys. 39 (1998), 6175.
Inozemtsev, V. I. and Mescheryakov, D. V.: Lett. Math. Phys. 9 (1985), 13; Inozemtsev, V. I.: Lett. Math. Phys. 17 (1989), 11–17.
Bordner, A. J., Corrigan, E. and Sasaki, R.: Progr. Theoret. Phys. 100 (1998), 1107–1129; 102 (1999), 499–529; Bordner, A. J., Sasaki, R. and Takasaki, K.: Progr. Theoret. Phys. 101 (1999), 487–518; Bordner, A. J. and Sasaki, R.: Progr. Theoret. Phys. 101 (1999), 799–829.
Avan, J. and Rollet, G.: J. Math. Phys. 43 (2002), to appear; nlin-SI/0106015.
Ruijsenaars, S.N.M.: Comm. Math. Phys. 115 (1988), 127.
Chen, K. and Hou, B.Y.: J. Phys. A 34 (2001), 7579–7590.
Chen, K., Hou, B.Y. and Yang, W.L.: Math. Phys. 41 (2000), 8132; 42 (2001), 4894–4914. 188
Feingold, A. J. and Frenkel, I. B.: Adv. Math., 56 (2) (1988), 117–172.
Gonera, C.: J. Phys. A, 31 (1998), 4465.
Gorsky, A. and Nekrasov, S.: Nuclear Phys. B 436 (1995), 582.
Semenov-Tjan-Shanskii, M. A.: RIMS Publ., 21 (6) (1985), 1237.
Drinfel'd, V. G.: Proc. I.C.M., MSRI Berkeley (1986), 798.
Alekseev, A. Yu. and Malkin, A. Z.: Comm. Math. Phys. 162 (1994), 147–174.
Olshanetskii, M. A. and Perelomov, A. M.: Phys. Rep. 71 (1981), 314.
Suris, Yu. B.: Phys. Lett., A 225 (1997), 223.
Babelon, O. and Viallet, C. M. Phys. Lett. B 237 (1990), 411.
Li, L. C. and Parmentier, S.: Comm. Math. Phys. 125 (1989), 545; Maillet, J.M.: Phys. Lett. B 167 (1986), 401; Freidel, L. and Maillet, J.M.: Phys. Lett. B 262 (1991), 278.
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Avan, J., Rollet, G. C (2) N+1 Ruijsenaars–Schneider Models. Letters in Mathematical Physics 60, 177–189 (2002). https://doi.org/10.1023/A:1016127325294
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DOI: https://doi.org/10.1023/A:1016127325294