Quantum versus classical integrability in Ruijsenaars-Schneider systems

Journal of Physics A: Mathematical and General

Volumn 37, Issue 2, 2004, Pages 469-479

  Ragnisco, O ^a   Sasaki, R ^b  

^a ROMA TRE UNIVERSITY   (Italy)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0742323577     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/37/2/015     Document Type: Conference Paper

References (31)

1. Corrigan E and Sasaki R 2002 Quantum vs classical integrability in Calogero-Moser systems J. Phys. A: Math. Gen. 35 7017-62 (Preprint hep-th/0204039) Odake S and Sasaki R 2002 Polynomials associated with equilibrium positions in Calogero-Moser systems J. Phys. A: Math. Gen. 35 8283-8314 (Preprint hep-th/0206172)
2. Corrigan E and Sasaki R 2002 Quantum vs classical integrability in Calogero-Moser systems J. Phys. A: Math. Gen. 35 7017-62 (Preprint hep-th/0204039) Odake S and Sasaki R 2002 Polynomials associated with equilibrium positions in Calogero-Moser systems J. Phys. A: Math. Gen. 35 8283-8314 (Preprint hep-th/0206172)
3. Calogero F 1971 Solution of the one-dimensional N-body problem with quadratic and/or inversely quadratic pair potentials J. Math. Phys. 12 419-36
4. Sutherland B 1972 Exact results for a quantum many-body problem in one-dimension: II Phys. Rev. A 5 1372-6
5. 2 ax) Lett. Nuovo Cimento 13 383-7 Calogero F 1975 Exactly solvable one-dimensional many body problems Lett. Nuovo Cimento 13 411-6
6. 2 ax) Lett. Nuovo Cimento 13 383-7 Calogero F 1975 Exactly solvable one-dimensional many body problems Lett. Nuovo Cimento 13 411-6
7. 2 ax) Lett. Nuovo Cimento 13 383-7 Calogero F 1975 Exactly solvable one-dimensional many body problems Lett. Nuovo Cimento 13 411-6
8. 2 ax) Lett. Nuovo Cimento 13 383-7 Calogero F 1975 Exactly solvable one-dimensional many body problems Lett. Nuovo Cimento 13 411-6
9. Olshanetsky M A and Perelomov A M 1976 Completely integrable Hamiltonian systems connected with semisimple Lie algebras Invent. Math. 37 93-108 Olshanetsky M A and Perelomov A M 1981 Classical integrable finite-dimensional systems related to Lie algebras Phys. Rep. C 71 314-400
10. Olshanetsky M A and Perelomov A M 1976 Completely integrable Hamiltonian systems connected with semisimple Lie algebras Invent. Math. 37 93-108 Olshanetsky M A and Perelomov A M 1981 Classical integrable finite-dimensional systems related to Lie algebras Phys. Rep. C 71 314-400
11. D'Hoker E and Phong D H 1998 Calogero-Moser Lax pairs with spectral parameter for general Lie algebras Nucl. Phys. B 530 537-610 (Preprint hep-th/9804124) Bordner A J, Corrigan E and Sasaki R 1998 Calogero-Moser models I: a new formulation Prog. Theor. Phys. 100 1107-29 (Preprint hep-th/9805106) Bordner A J, Corrigan E and Sasaki R 1999 Generalized Calogero-Moser models and universal Lax pair operators Prog. Theor. Phys. 102 499-529 (Preprint hep-th/9905011)
12. D'Hoker E and Phong D H 1998 Calogero-Moser Lax pairs with spectral parameter for general Lie algebras Nucl. Phys. B 530 537-610 (Preprint hep-th/9804124) Bordner A J, Corrigan E and Sasaki R 1998 Calogero-Moser models I: a new formulation Prog. Theor. Phys. 100 1107-29 (Preprint hep-th/9805106) Bordner A J, Corrigan E and Sasaki R 1999 Generalized Calogero-Moser models and universal Lax pair operators Prog. Theor. Phys. 102 499-529 (Preprint hep-th/9905011)
13. D'Hoker E and Phong D H 1998 Calogero-Moser Lax pairs with spectral parameter for general Lie algebras Nucl. Phys. B 530 537-610 (Preprint hep-th/9804124) Bordner A J, Corrigan E and Sasaki R 1998 Calogero-Moser models I: a new formulation Prog. Theor. Phys. 100 1107-29 (Preprint hep-th/9805106) Bordner A J, Corrigan E and Sasaki R 1999 Generalized Calogero-Moser models and universal Lax pair operators Prog. Theor. Phys. 102 499-529 (Preprint hep-th/9905011)
14. Bordner A J, Manton N S and Sasaki R 2000 Calogero-Moser models V: supersymmetry and quantum Lax pair Prog. Theor. Phys. 103 463-87 (Preprint hep-th/9910033) Khastgir S P, Pocklington A J and Sasaki R 2000 Quantum Calogero-Moser models: integrability for all root systems J. Phys. A: Math. Gen. A 33 9033-64 (Preprint hep-th/0005277)
15. Bordner A J, Manton N S and Sasaki R 2000 Calogero-Moser models V: supersymmetry and quantum Lax pair Prog. Theor. Phys. 103 463-87 (Preprint hep-th/9910033) Khastgir S P, Pocklington A J and Sasaki R 2000 Quantum Calogero-Moser models: integrability for all root systems J. Phys. A: Math. Gen. A 33 9033-64 (Preprint hep-th/0005277)
16. Ruijsenaars S N and Schneider H 1986 A new class of integrable systems and its relation to solitons Ann. Phys., NY 170 370-405 Ruijsenaars S N and Schneider H 1987 Complete integrability of relativistic Calogero-Moser systems and elliptic function identities Commun. Math. Phys. 110 191
17. Ruijsenaars S N and Schneider H 1986 A new class of integrable systems and its relation to solitons Ann. Phys., NY 170 370-405 Ruijsenaars S N and Schneider H 1987 Complete integrability of relativistic Calogero-Moser systems and elliptic function identities Commun. Math. Phys. 110 191
18. van Diejen J F 1995 The relativistic Calogero model in an external field Preprint solv-int/9509002 van Diejen J F 1995 Multivariable continuous Hahn and Wilson polynomials related to integrable difference systems J. Phys. A: Math. Gen. 28 L369-74
19. van Diejen J F 1995 The relativistic Calogero model in an external field Preprint solv-int/9509002 van Diejen J F 1995 Multivariable continuous Hahn and Wilson polynomials related to integrable difference systems J. Phys. A: Math. Gen. 28 L369-74
20. van Diejen J F 1995 Difference Calogero-Moser systems and finite Toda chains J. Math. Phys. 36 1299-323
21. van Diejen J F 1994 Integrability of difference Calogero-Moser systems J. Math. Phys. 35 2983-3004
22. Braden H W and Sasaki R 1997 The Ruijsenaars-Schneider model Prog. Theor. Phys. 97 1003-18 (Preprint hep-th/9702182)
23. Andrews G E, Askey R and Roy R 1999 Special Functions (Encyclopedia of Mathematics and Its Applications vol 11) (Cambridge: Cambridge University Press)
24. Calogero F 2001 Classical Many-Body Problems Amenable to Exact Treatments (Springer: Berlin)
25. Macdonald I G 2000 Orthogonal polynomials associated with root systems Séminaire Lotharingien de Combinatoire 45 article B45a Macdonald I G 2000 Séminaire Lotharingien de Combinatoire 45 article B45a
26. Macdonald I G 2000 Orthogonal polynomials associated with root systems Séminaire Lotharingien de Combinatoire 45 article B45a Macdonald I G 2000 Séminaire Lotharingien de Combinatoire 45 article B45a
27. Jack H 1979 A class of symmetric polynomials with a parameter Proc. R. Soc. Edin. A 69 1-18
28. Ruijsenaars S N 1995 Action-angle maps and scattering theory for some finite-dimensional integrable systems: in, Sutherland type systems and their duals Publ. Res. Inst. Math. Sci. 31 247-353
29. n Ruijsenaars-Schneider model J. Phys. A: Math. Gen. 34 7579-89 (Preprint hep-th/0102036)
30. n Ruijsenaars-Schneider model J. Phys. A: Math. Gen. 34 7579-89 (Preprint hep-th/0102036)
31. n Ruijsenaars-Schneider model J. Phys. A: Math. Gen. 34 7579-89 (Preprint hep-th/0102036)