{"title":"Consistency of the Bäcklund Transformation for the Spin Calogero–Moser System","authors":"Bjorn K. Berntson","doi":"10.1007/s11040-023-09450-z","DOIUrl":null,"url":null,"abstract":"<div><p>We prove the consistency of the Bäcklund transformation (BT) for the spin Calogero–Moser (sCM) system in the rational, trigonometric, and hyperbolic cases. The BT for the sCM system consists of an overdetermined system of ordinary differential equations; to establish our result, we construct and analyze certain functions that measure the departure of this overdetermined system from consistency. We show that these functions are identically zero and that this allows for a unique solution to the initial value problem for the overdetermined system.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"26 2","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-023-09450-z.pdf","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Physics, Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s11040-023-09450-z","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
Abstract
We prove the consistency of the Bäcklund transformation (BT) for the spin Calogero–Moser (sCM) system in the rational, trigonometric, and hyperbolic cases. The BT for the sCM system consists of an overdetermined system of ordinary differential equations; to establish our result, we construct and analyze certain functions that measure the departure of this overdetermined system from consistency. We show that these functions are identically zero and that this allows for a unique solution to the initial value problem for the overdetermined system.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
