带约束的B型和变形rujsenaars - schneider系统Toda格的椭圆解

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2023-08-03 DOI:10.1007/s11040-023-09462-9

V. Prokofev, A. Zabrodin

{"title":"带约束的B型和变形rujsenaars - schneider系统Toda格的椭圆解","authors":"V. Prokofev, A. Zabrodin","doi":"10.1007/s11040-023-09462-9","DOIUrl":null,"url":null,"abstract":"<div><p>We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars–Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By studying more general elliptic solutions (elliptic families), we also suggest an extension of the deformed Ruijsenaars–Schneider system to a field theory.\n</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Elliptic Solutions of the Toda Lattice with Constraint of Type B and Deformed Ruijsenaars–Schneider System\",\"authors\":\"V. Prokofev, A. Zabrodin\",\"doi\":\"10.1007/s11040-023-09462-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars–Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By studying more general elliptic solutions (elliptic families), we also suggest an extension of the deformed Ruijsenaars–Schneider system to a field theory.\\n</p></div>\",\"PeriodicalId\":694,\"journal\":{\"name\":\"Mathematical Physics, Analysis and Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-08-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Physics, Analysis and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11040-023-09462-9\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Physics, Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s11040-023-09462-9","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 1

摘要

我们研究了最近引入的带有B型约束的Toda格的椭圆解，并推导了其极点的运动方程。极点动力学是由变形的rujsenaars - schneider系统给出的。我们找到了它的Manakov三重形式的对易表示，并研究了谱曲线的性质。通过研究更一般的椭圆解(椭圆族)，我们还提出了将变形rujsenaars - schneider系统推广到场理论的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Elliptic Solutions of the Toda Lattice with Constraint of Type B and Deformed Ruijsenaars–Schneider System

We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars–Schneider system. We find its commutation representation in the form of the Manakov triple and study properties of the spectral curve. By studying more general elliptic solutions (elliptic families), we also suggest an extension of the deformed Ruijsenaars–Schneider system to a field theory.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.