Generalized model of interacting integrable tops

Grekov, A.; Сечин, Иван Андреевич; Zotov, A.

doi:10.1007/jhep10(2019)081

Cited by 14 publications

(6 citation statements)

References 82 publications

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“…In the elliptic case the above given Lax pairs and equations of motion are reproduce 1 the results of our previous paper [17], and in the non-relativistic limit the results of [6] are reproduced as well. For N = 1 the R-matrix operators under consideration become the scalar functions from (1.1), thus reproducing the spin Ruijsenaars-Schneider model (1.21)-(1.27).…”

Section: )supporting

confidence: 81%

“…In the non-relativistic elliptic case the models of the above described type were first obtained in [10], They were later described as Hitchin systems on the bundles with non-trivial characteristic classes [8]. Some explicit examples of the systems can be easily obtained using R-matrices used in [6] in the same normalization as in the present article.…”

Section: )mentioning

confidence: 87%

“…This paper is a continuation of series of articles [6,14,17], where known integrable systems and related structures are extended through the use of quantum R-matrices (in the fundamental representation of GL(N) Lie groups) being interpreted as matrix generalizations of the Kronecker function. It is convenient to give its explicit form the very beginning in the rational, trigonometric and elliptic cases since the identities to be used are valid in all these cases: All the functions are complex valued.…”

Section: Introductionmentioning

confidence: 99%

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Integrable system of generalized relativistic interacting tops

Сечин

Zotov

2020

Theor Math Phys

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A family of integrable GL(N M) models is described. On the one hand it generalizes the classical spin Ruijsenaars-Schneider systems (the case N = 1), and on the other hand it generalizes the relativistic integrable tops on GL(N) Lie group (the case M = 1). The described models are obtained by means of the Lax pair with spectral parameter. Equations of motion are derived. For the construction of the Lax representation the GL(N) R-matrix in the fundamental representation of GL(N) is used.

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Section: )supporting

confidence: 81%

Section: )mentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

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Integrable system of generalized relativistic interacting tops

Сечин

Zotov

2020

Theor Math Phys

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“…Such a Lax pair allows one to calculate the higher Hamiltonians. These questions will be discussed in our next publication [21].…”

Section: Discussionmentioning

confidence: 97%

On R-matrix valued Lax pairs for Calogero–Moser models

Grekov¹,

Zotov²

2018

J. Phys. A: Math. Theor.

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The article is devoted to the study of R-matrix-valued Lax pairs for N -body (elliptic) Calogero-Moser models. Their matrix elements are given by quantum GLÑ R-matrices of Baxter-Belavin type. ForÑ = 1 the widely known Krichever's Lax pair with spectral parameter is reproduced. First, we construct the R-matrix-valued Lax pairs for Calogero-Moser models associated with classical root systems. For this purpose we study generalizations of the D'Hoker-Phong Lax pairs. It appeared that in the R-matrix-valued case the Lax pairs exist in special cases only. The number of quantum spaces (on which R-matrices act) and their dimension depend on the values of coupling constants. Some of the obtained classical Lax pairs admit straightforward extension to the quantum case. In the end we describe a relationship of the R-matrix-valued Lax pairs to Hitchin systems defined on SL NÑ bundles with nontrivial characteristic classes over elliptic curve. We show that the classical analogue of the anisotropic spin exchange operator entering the R-matrix-valued Lax equations is reproduced in these models.

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“…In this respect the associative Yang-Baxter equation unifies classical and quantum integrable structures. See [15][16][17] and references therein.…”

Section: Explicit Change Of Variables 1 Introductionmentioning

confidence: 99%

Field analogue of the Ruijsenaars-Schneider model

Zabrodin

Zotov²

2022

J. High Energ. Phys.

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We suggest a field extension of the classical elliptic Ruijsenaars-Schneider model. The model is defined in two different ways which lead to the same result. The first one is via the trace of a chain product of L-matrices which allows one to introduce the Hamiltonian of the model and to show that the model is gauge equivalent to a classical elliptic spin chain. In this way, one obtains a lattice field analogue of the Ruijsenaars-Schneider model with continuous time. The second method is based on investigation of general elliptic families of solutions to the 2D Toda equation. We derive equations of motion for their poles, which turn out to be difference equations in space with a lattice spacing η, together with a zero curvature representation for them. We also show that the equations of motion are Hamiltonian. The obtained system of equations can be naturally regarded as a field generalization of the Ruijsenaars-Schneider system. Its lattice version coincides with the model introduced via the first method. The limit η → 0 is shown to give the field extension of the Calogero-Moser model known in the literature. The fully discrete version of this construction is also discussed.

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Generalized model of interacting integrable tops

Cited by 14 publications

References 82 publications

Integrable system of generalized relativistic interacting tops

Integrable system of generalized relativistic interacting tops

On R-matrix valued Lax pairs for Calogero–Moser models

Field analogue of the Ruijsenaars-Schneider model

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