Universality of Calogero-Moser model

Journal of Nonlinear Mathematical Physics

Volumn 12, Issue SUPPL. 1, 2005, Pages 522-534

  Olshanetsky, M A ^a,b  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29344451508     PISSN: 14029251     EISSN: 14029251     Source Type: Journal    
DOI: 10.2991/jnmp.2005.12.s1.42     Document Type: Review

References (40)

1. H.Airault, H.McKean, J.Moser, Rational and elliptic solutions of the Korteweg-de Vries equation and a related many-body problem, Comm. Pure Appl. Math. 30 (1977), no. 1, 95-148.
2. H.Azuma, S.Iso, Explicit Relation of Quantum Hall Effect and Calogero-Sutherland Model, Phys. Lett. B, B331 (1994) 107-113.
3. A.Babich and L.Bordag, The elliptic form of the sixth Painlevé equation, Preprint NTZ 25/1997.
4. D.Bernard, On the Wess-Zumino-Witten models on the torus, Nucl.Phys. B303 (1988) 77.
5. F.Calogero, Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials, J. Mathematical Phys. 12 (1971) 419-436.
6. F.Calogero, Exactly solvable one dimensional many-body problem, Lettere al Nuovo Cimento, 13 (1975) 411-416.
7. P.Etingof, A.Kirillov, Jr., Representations of affine Lie algebras, parabolic differential equations, and Lame functions, Duke Math. J. 74 (1994), no. 3, 585-614.
8. B.Enriquez, V.Rubtsov, Hitchin systems, higher Gaudin operators and R-matrices, Math. Res. Lett, 3 (1996), 343-357.
9. G.Felder, A.Varchenko, Integral representation of solutions of the Knizhnik-Zamolodchikov Bernard equations, Intern. Math. Res. Notices (1995) no. 5, 221-233.
10. J.Gibbons and T.Hermsen, A generalization of Calogero-Moser system, Physica D 11D (1984) 337.
11. A.Gorsky, I.Krichever, A.Marshakov, A.Mironov, A.Morozov, Integrability and Seiberg-Witten Exact Solution, Phys.Lett.B, B355 (1995) 466-474.
12. A.Gorsky, N.Nekrasov, Elliptic Calogero-Moser system from two dimensional current algebra, [hep-th/9401021].
13. N. Hitchin, Stable bundles and Integrable Systems, Duke Math. Journ., 54 (1987) 91-114.
14. D.Ivanov, KZB eqs. as a quantization of nonstationary Hitchin systems, [hep-th/9610207].
15. V.Inozemtsev, Lax Representation with spectral parameter on a torus for integrable particle systems, Lett. Math. Phys., 17 (1989) 11-17.
16. V.Inozemtsev, R.Sasaki, Hierarchies of Spin Models related to Calogero-Moser Models, Nucl.Phys., B618 (2001) 689-698.
17. D.Kazhdan, B.Kostant, S.Sternberg, Hamiltonian group actions and dynamical systems of Calogero type, Comm. Pure Appl. Math. 31 (1978), 481-507.
18. I.Krichever, Elliptic solutions of the Kadomcev-Petviašvili equations, and integrable systems of particles, Funktsional. Anal. i Prilozhen. 14 (1980), no. 4, 45-54.
19. I.Krichever, Vector bundles and Lax equations on algebraic curves, Comm. Math. Phys., 229 (2002), no. 2, 229-269.
20. V.Knizhnik and A.Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nucl.Phys. B247 (1984) 83.
21. G.Kuroki, T.Takebe, Wess-Zumino-Witten model on elliptic curves at the critical level, J. Phys. A, 34 (2001), no. 11, 2403-2413.
22. A.Levin, M.Olshanetsky, Hierarchies of isomonodromic deformations and Hitchin systems. Moscow Seminar in Mathematical Physics, Amer. Math. Soc. Transl. Ser. 2, 191 Amer. Math. Soc., Providence, RI, (1999) 223-262.
23. A.Levin, M.Olshanetsky, A.Zotov, Hitchin systems- symplectic Hecke correspondence and two-dimensional version, Comm. Math. Phys., 236 (2003), 93-133.
24. J.Moser, Three integrable Hamiltonian systems connected with isospectral deformations, Advances in Math. 16 (1975), 197-220.
25. Yu.I.Manin, Sixth Painlevé equation, universal elliptic curve, and mirror of P2, Amer. Math. Soc. Transl. (2), 186 (1998) 131-151.
26. E.Markman, Spectral curves and integrable systems, Comp. Math., 93 (1994) 255-290.
27. N.Nekrasov, Holomorphic bundles and many-body systems, Comm. Math. Phys., 180 (1996), 587-604.
28. M.Olshanetsky, A.Perelomov, Completely integrable Hamiltonian systems connected with semisimple Lie algebras. Invent. Math. 37 (1976), 93-108.
29. M.Olshanetsky, A.Perelomov, Classical integrable finite-dimensional systems related to Lie algebras, Phys. Rep., 71 (1981), 313-400.
30. M.Olshanetsky, A.Perelomov, Quantum integrable systems related to Lie algebras, Phys. Rep., 94 (1983), 313-404.
31. M.Olshanetsky, A.Perelomov, Explicit solution of the Calogero model in the classical case and geodesic flows on symmetric spaces of zero curvature, Lett. Nuovo Cimento (2) 16 (1976), 333-339.
32. M.Olshanetsky, A.Perelomov, Explicit solutions of some completely integrable systems, Lett. Nuovo Cimento (2) 17 (1976), 97-101.
33. M.Olshanetsky, A.Perelomov, Quantum completely integrable systems connected with semi-simple Lie algebras, Lett. Math. Phys., 2 (1977/78), 7-13.
34. Painlevé, Sur les équations différentielles du second odre à points critics fixes, CRAS, 143 (1906) 1111-1117.
35. A.G. Reyman, M.A Semenov-Tyan-Shanskii, Lie algebras and Lax equations with spectral parameter on elliptic curve, Notes from Sci. Seminar LOMI, Vol. 150, (1986), 104-118.
36. B.Sutherland, J. Math. Phys. 12 (1971) 246-251;
37. Phys. Rev., A4 (1971) 2019,
38. Phys. Rev., A5 (1972) 1372.
39. 2 and Superconformal Matrix Quantum Mechanics, [hep-th/0403024].
40. A.Zotov, Elliptic Linear Problem for Calogero-Inozemtsev Model and Painleve VI Equation Lett.Math.Phys., 67 (2004) 153-165.