A generalisation of the Calogero-Moser system

Gibbons, John; Hermsen, Theo

doi:10.1016/0167-2789(84)90015-0

Cited by 214 publications

(262 citation statements)

References 7 publications

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“…[4] to us. His explanation of the results of these papers helped us to resolve a difficulty which had prevented us from completing this work earlier.…”

Section: Acknowledgmentmentioning

confidence: 99%

“…A well-known example is v(r) ∝ g 2 / sin 2 (gr) (which includes v(r) ∝ 1/r 2 in the limit g → 0), and we refer to the corresponding model as CS model. It is known that these models allow for interesting generalizations which also have dynamic spin degrees of freedom [4,5]. The CS model and its generalizations have recently received quite some attention in different contexts.…”

Section: Introductionmentioning

confidence: 99%

“…In this article we find and solve a new class of integrable systems containing the CS model and their spin-generalizations [4] as limiting cases. Our method is to extend and exploit the relation of the CS model to gauge theories on a cylinder, as will be explained in detail below.…”

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confidence: 99%

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Novel integrable spin-particle models from gauge theories on a cylinder

Blom¹,

Langmann²

1998

Physics Letters B

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We find and solve a large class of integrable dynamical systems which includes Calogero-Sutherland models and various novel generalizations thereof. In general they describe N interacting particles moving on a circle and coupled to an arbitrary number, m, of su(N ) spin degrees of freedom with interactions which depend on arbitrary real parameters x j , j = 1, 2, . . . , m. We derive these models from SU(N ) Yang-Mills gauge theory coupled to non-dynamic matter and on spacetime which is a cylinder. This relation to gauge theories is used to prove integrability, to construct conservation laws, and solve these models.Integrable models have always played a central role in classical and quantum mechanics. Most prominent examples, like the Kepler problem, are systems with few (≤ 3) degrees of freedom. An important exception is a class of integrable N-particle models associated with the names Calogero, Moser and Sutherland [1, 2] (for review see [3]). These are models for identical particles moving on one dimensional space and interacting via certain repulsive twobody potentials v(r). A well-known example is v(r) ∝ g 2 / sin 2 (gr) (which includes v(r) ∝ 1/r 2 in the limit g → 0), and we refer to the corresponding model as CS model. It is known that these models allow for interesting generalizations which also have dynamic spin degrees of freedom [4,5]. The CS model and its generalizations have recently received quite some attention in different contexts. Here we only mention their relation to gauged matrix models [6] and gauge theories on a cylinder [7] which will be relevant for us. a a the latter relation is implicit already in earlier work; see e.g. [8]

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“…[4] to us. His explanation of the results of these papers helped us to resolve a difficulty which had prevented us from completing this work earlier.…”

Section: Acknowledgmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Novel integrable spin-particle models from gauge theories on a cylinder

Blom¹,

Langmann²

1998

Physics Letters B

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“…This section is a concise version of [26]. Spin generalization of the Calogero-Moser system was first found in [15]. The better title of this section would be spin Calogero-Moser-Sutherland-Olshanetsky-Perelomov systems [3] [19][29] [22].…”

Section: Introductionmentioning

confidence: 99%

Degenerately Integrable Systems

Reshetikhin

2016

J Math Sci

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Abstract. The subject of this paper is degenerate integrability in Hamiltonian mechanics. It starts with a short survey of degenerate integrability. The first section contains basic notions. It is followed by a number of examples which include the Kepler system, Casimir models, spin Calogero models, spin Ruijsenaars models, and integrable models on symplectic leaves of Poisson Lie groups. The new results are degenerate integrability of relativistic spin Ruijsenaars and Calogero-Moser systems and the duality between them.

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“…The connection of the matrix model to the Calogero model along the lines presented here and below was first established in [35]. Also, the hamiltonian (60) has been proposed independently of the matrix model as an SU(N)-generalization of the classical Calogero system [36,37].…”

Section: Hermitian Matrix Modelmentioning

confidence: 99%

Generalized Statistics in One Dimension

Polychronakos

Aspects Topologiques De La Physique en Basse Dimension. Topological Aspects of Low Dimensional Systems

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A generalisation of the Calogero-Moser system

Cited by 214 publications

References 7 publications

Novel integrable spin-particle models from gauge theories on a cylinder

Novel integrable spin-particle models from gauge theories on a cylinder

Degenerately Integrable Systems

Generalized Statistics in One Dimension

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