Quantum integrable systems related to lie algebras

Olshanetsky, M.; Perelomov, A. M.

doi:10.1016/0370-1573(83)90018-2

Cited by 896 publications

(1,083 citation statements)

References 61 publications

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“…These relativistic particle systems are not only completely integrable at the classical level, but can also be quantized in such a fashion that integrability survives [1,2]. In this paper we show that relativistic integrable generalizations of the nonrelativistic Toda systems [3][4][5] exist, too. Moreover, we solve the nonperiodic classical systems by constructing an explicit action-angle transformation.…”

Section: Introductionmentioning

confidence: 74%

Relativistic Toda systems

Ruijsenaars¹

1990

Commun.Math. Phys.

243

306

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Section: Introductionmentioning

confidence: 74%

Relativistic Toda systems

Ruijsenaars¹

1990

Commun.Math. Phys.

243

306

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“…note, in particular, that the set A properly contains the BC N configuration space (4). Similarly (cf.…”

Section: The Modelsmentioning

confidence: 80%

“…Recent studies have revealed that exactly solvable and integrable one-dimensional quantum many body systems with long-range interactions [1][2][3][4][5][6][7][8] are closely connected with a wide range of topics in modern physics as well as mathematics. In particular, this type of exactly solv-able systems have appeared as prototype models of various condensed matter systems exhibiting generalized exclusion statistics [8][9][10], quantum Hall effect [11] and quantum electric transport phenomena [12,13].…”

Section: Introductionmentioning

confidence: 99%

The spin Sutherland model of type and its associated spin chain

2011

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In this paper we study the su(m) spin Sutherland (trigonometric) model of D N type and its related spin chain of Haldane-Shastry type obtained by means of Polychronakos's freezing trick. As in the rational case recently studied by the authors, we show that these are new models, whose properties cannot be simply deduced from those of their well-known BC N counterparts by taking a suitable limit. We identify the Weyl-invariant extended configuration space of the spin dynamical model, which turns out to be the N-dimensional generalization of a rhombic dodecahedron. This is in fact one of the reasons underlying the greater complexity of the models studied in this paper in comparison with both their rational and BC N counterparts. By constructing a non-orthogonal basis of the Hilbert space of the spin dynamical model on which its Hamiltonian acts triangularly, we compute its spectrum in closed form. Using this result and applying the freezing trick, we derive an exact expression for the partition function of the associated Haldane-Shastry spin chain of D N type.

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“…The systems just delineated were surveyed in the early eighties by 01-shanetsky and Perelomov, both in the classical [1] and in the quantum context [2]. These surveys contain extensive lists of references, and arc to a large extent concerned with the relations of the systemi:; to group theory, Lie algebra theory, and harmonic analysis on symmetric spaces.…”

Section: Introductionmentioning

confidence: 99%

Systems of Calogero-Moser Type

Ruijsenaars¹

1999

Particles and Fields

102

161

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We survey results on Galilei-and Poincare-invariant CalogeroMoser and Toda N-particle systems, both in the context of classical mc hanics and of quantum mechanics. Special attention is given to integrability issues and interconnections between the various models. Action-angle and joint eigenfunction transforms are also considered, and some novel results on N = 2 eigenfunctions of hyperbolic Askey-Wilson type and of relativistic elliptic type are sketched.

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Quantum integrable systems related to lie algebras

Cited by 896 publications

References 61 publications

Relativistic Toda systems

Relativistic Toda systems

The spin Sutherland model of type and its associated spin chain

Systems of Calogero-Moser Type

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