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Quantum Calogero-Moser Model and its Algebraic Structures (統計物理学の展開と応用--多様性の中の類似性(研究会報告))

Miki Wadati, Hideaki Ujino, Kazuhiro Hikami

物性研究Jul 20, 19931 citation

Hierarchies of spin models related to Calogero–Moser models

V. I. Inozemtsev, Ryu Sasaki B

arXiv:hep-th/0105197Nuclear Physics BDec 1, 20014 citations

Dynamical r-matrices and separation of variables: the generalized Calogero-Moser model

Tomasz Brzeziński

arXiv:hep-th/9401049Physics Letters BApr 1, 19947 citations

Algebra of one-particle operators for the Calogero model

Serguei B. Isakov, Jon Magne Leinaas

arXiv:hep-th/9510184Nuclear Physics BMar 1, 199616 citations

The Quantum Calogero-Moser Model: Algebraic Structures

Hideaki Ujino, Miki Wadati, Kazuhiro Hikami

For the quantum Calogero-Moser model, we construct a set of conserved operators and another set of operators, named boost operators, from its Lax operator. We prove that each conserved operator satisfies both the Lax equation and a remarkable relation named additional relation. From these knowledge, we show that the conserved operators are involutive. Moreover, the conserved operators and the boost operators constitute the U(1)-current algebra. All the proofs are simplified a great deal due to the Lax equations and additional relations.For the quantum Calogero-Moser model, we construct a set of conserved operators and another set of operators, named boost operators, from its Lax operator. We prove that each conserved operator satisfies both the Lax equation and a remarkable relation named additional relation. From these knowledge, we show that the conserved operators are involutive. Moreover, the conserved operators and the boost operators constitute the U(1)-current algebra. All the proofs are simplified a great deal due to the Lax equations and additional relations.

Journal of the Physical Society of JapanSep 15, 199343 citations

Quantum-classical duality for Gaudin magnets with boundary

M. Vasilyev, Anton Vladimirovich Zabrodin, Andrei Vladimirovich Zotov

We establish a remarkable relationship between the quantum Gaudin models with boundary and the classical many-body integrable systems of Calogero-Moser type associated with the root systems of classical Lie algebras (B, C and D). We show that under identification of spectra of the Gaudin Hamiltonians HjG with particles velocities q˙j of the classical model all integrals of motion of the latter take zero values. This is the generalization of the quantum-classical duality observed earlier for Gaudin models with periodic boundary conditions and Calogero-Moser models associated with the root system of the type A.We establish a remarkable relationship between the quantum Gaudin models with boundary and the classical many-body integrable systems of Calogero-Moser type associated with the root systems of classical Lie algebras (B, C and D). We show that under identification of spectra of the Gaudin Hamiltonians HjG with particles velocities q˙j of the classical model all integrals of motion of the latter take zero values. This is the generalization of the quantum-classical duality observed earlier for Gaudin models with periodic boundary conditions and Calogero-Moser models associated with the root system of the type A.

arXiv:1911.11792Nuclear Physics BJan 21, 20204 citations

Integrability and algebraic structure of the quantum Calogero-Moser model

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