Remarks on integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models

2024/03/14 by Anton Galajinsky, Galajinsky, Anton · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2403.09204

openalex publication_date 2024/03/14 · openalex created_date 2024/03/16 · openalex updated_date 2026/07/28

Abstract

Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models based upon the potentials W(x)=2/x, W(x)=2/sin(x), and W(x)=2/sinh(x) is proven. The problem of constructing an algebraically resolvable set of Grassmann-odd constants of motion is reduced to finding a triplet of vectors such that all their scalar products can be expressed in terms of the original bosonic first integrals. The supersymmetric generalizations are used to build novel integrable (iso)spin extensions of the respective Ruijsenaars-Schneider three-body systems.

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