@article{ZNSL_2015_433_a11,
author = {N. Reshetikhin},
title = {Degenerately integrable systems},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {224--245},
year = {2015},
volume = {433},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_433_a11/}
}
N. Reshetikhin. Degenerately integrable systems. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 23, Tome 433 (2015), pp. 224-245. http://geodesic.mathdoc.fr/item/ZNSL_2015_433_a11/
[1] A. Alekseev, E. Meinrenken, C. Woodward, “Group-valued equivariant localization”, Invent. Math., 140:2 (2000), 327–350 | DOI | MR | Zbl
[2] V. Ayadi, L. Feher, T. F. J. Gorbe, “Superintegrability of rational Ruijsenaars–Schneider systems and their action-angle duals”, Geom. Symmetry Phys., 27 (2012), 27–44 | MR | Zbl
[3] F. Calogero, “Solution of the one-dimensional N-body problem with quadratic and/or in-versely quadratic pair potentials”, J. Math. Phys., 12 (1971), 419–436 | DOI | MR
[4] B. Enriquez, V. Rubtsov, “Hitchin systems, higher Gaudin operators and $R$-matrices”, Math. Res. Lett., 3:3 (1996), 343–357 | DOI | MR | Zbl
[5] L. Feher, B. G. Pusztai, “Twisted spin Sutherland models from quantum Hamiltonian reduction”, J. Phys. A, 41:19 (2008), 194009 | DOI | MR | Zbl
[6] L. Feher,B. G. Pusztai, “Generalized spin Sutherland systems revisited”, Nucl. Phys. B, 893 (2015), 236–256 | DOI | MR
[7] V. Fock, A. Gorsky, N. Nekrasov, A. Rubtsov, “Dualities in Integrable Gauge Theories”, JHEP, 028 (2000), 0007
[8] V. Fock, “Zur Theorie des Wasserstoffatoms”, Z. Physik, 98 (1935), 145 | DOI | Zbl
[9] Theoret. and Math. Phys., 95:2 (1993), 526–534 | DOI | MR | Zbl
[10] A. S. Mischenko, A. T. Fomenko, “Generalized Liouville method or integrating Hamiltonian systems”, Funct. Anal. Appl., 12:2 (1978), 46–56 | MR | Zbl
[11] J. Frish, V. Mandrosov, Y. A. Smorodinsky, M. Uhlir, P. Winternitz, “On higher symmetries in quantum mechanics”, Physics Letters, 16 (1965), 354–356 | DOI | MR
[12] M. I. Gekhtman, M. Z. Shapiro, “Non-commutative and commutative integrability of generic Toda flow in simple Lie algberas”, Comm. Pure Appl. Math., 52 (1999), 53–84 | 3.0.CO;2-5 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl
[13] J. Gibbons, T. Hermsen, “A generalization of the Calogero–Moser system”, Physica D, 11 (1984), 337 | DOI | MR | Zbl
[14] D. Kazhdan, B. Kostant, S. Sternberg, “Hamiltonian group actions and dynamical systems of Calogero type”, Comm. Pure Appl. Math., 31:4 (1978), 481–507 | DOI | MR | Zbl
[15] I. Krichever, O. Babelon, E. Billey, M. Talon, “Spin generalization of the Calogero–Moser system and the matrix KP equation”, Topics in Topology and Math. Phys., Amer. Math. Soc. Transl. Ser. 2, 170, Amer. Math. Soc., 1995, 83–119 ; arXiv: hep-th/9411160 | MR | Zbl
[16] L. C. Li, P. Xu, “Spin Calogero–Moser systems associated with simple Lie algebras”, C. R. Acad. Sci. Ser. I, 331:1 (2000), 55–61 | MR
[17] J. Moser, “Three integrable Hamiltonian systems connected with isospectral deformations”, Advances in Math., 16 (1975), 197–220 | DOI | MR | Zbl
[18] N. N. Nekhoroshev, “Action-angle variables and their generalizations”, Trans. Moscow Math. Soc., 26 (1972), 180–197 | MR
[19] N. Nekrasov, “Holomorphyc bundles and many-body systems”, CMP, 180 (1996), 587–604 | MR
[20] M. A. Olshanetsky, A. M. Perelomov, “Quantum integrable systems related to Lie algebras”, Phys. Rept., 94 (1983), 313–404 | DOI | MR
[21] W. Pauli, “On the hydrogen spectrum from the standpoint of the new quantum mechanics”, Z. Physik, 36 (1926), 336–363 | DOI | Zbl
[22] W. Pauli, Z. Physik, 36 (1935), 336
[23] N. Reshetikhin, “Integrability of characteristic Hamiltonian systems on simple Lie groups with standard Poisson Lie structure”, Comm. Math. Phys., 242:1–2 (2003), 1–29 | DOI | MR | Zbl
[24] N. Reshetikhin, “Degenerate integrability of the spin Calogero–Moser systems and the duality with the spin Ruijsenaars systems”, Lett. Math. Phys., 63:1 (2003), 55–71 | DOI | MR | Zbl
[25] M. Semenov-Tian-Shansky, “Dressing transformations and Poisson group actions”, Publ. Res. Inst. Math. Sci., 21 (1985), 1237–1260 | DOI | MR | Zbl
[26] B. Sutherland, “Exact results for a many-body problem in one dimension. II”, Phys. Rev. A, 5:3 (1972), 1372–1376 | DOI | MR
[27] S. Wojciechowski, “Superintegrability of the Calogero–Moser system”, Phys. Lett. A, 95 (1983), 279 | DOI | MR