{"title":"关于 N=1 超对称鲁伊塞纳尔斯-施耐德三体模型可整性的评论","authors":"Anton Galajinsky","doi":"arxiv-2403.09204","DOIUrl":null,"url":null,"abstract":"Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models\nbased upon the potentials W(x)=2/x, W(x)=2/sin(x), and W(x)=2/sinh(x) is\nproven. The problem of constructing an algebraically resolvable set of\nGrassmann-odd constants of motion is reduced to finding a triplet of vectors\nsuch that all their scalar products can be expressed in terms of the original\nbosonic first integrals. The supersymmetric generalizations are used to build\nnovel integrable (iso)spin extensions of the respective Ruijsenaars-Schneider\nthree-body systems.","PeriodicalId":501592,"journal":{"name":"arXiv - PHYS - Exactly Solvable and Integrable Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Remarks on integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models\",\"authors\":\"Anton Galajinsky\",\"doi\":\"arxiv-2403.09204\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models\\nbased upon the potentials W(x)=2/x, W(x)=2/sin(x), and W(x)=2/sinh(x) is\\nproven. The problem of constructing an algebraically resolvable set of\\nGrassmann-odd constants of motion is reduced to finding a triplet of vectors\\nsuch that all their scalar products can be expressed in terms of the original\\nbosonic first integrals. The supersymmetric generalizations are used to build\\nnovel integrable (iso)spin extensions of the respective Ruijsenaars-Schneider\\nthree-body systems.\",\"PeriodicalId\":501592,\"journal\":{\"name\":\"arXiv - PHYS - Exactly Solvable and Integrable Systems\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Exactly Solvable and Integrable Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2403.09204\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Exactly Solvable and Integrable Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2403.09204","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Remarks on integrability of N=1 supersymmetric Ruijsenaars-Schneider three-body models
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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