{"title":"Integrability of \\( \\Phi ^4\\) matrix model as N-body harmonic oscillator system","authors":"Harald Grosse, Akifumi Sako","doi":"10.1007/s11005-024-01783-2","DOIUrl":null,"url":null,"abstract":"<div><p>We study a Hermitian matrix model with a kinetic term given by <span>\\( Tr (H \\Phi ^2 )\\)</span>, where <i>H</i> is a positive definite Hermitian matrix, similar as in the Kontsevich Matrix model, but with its potential <span>\\(\\Phi ^3\\)</span> replaced by <span>\\(\\Phi ^4\\)</span>. We show that its partition function solves an integrable Schrödinger-type equation for a non-interacting <i>N</i>-body Harmonic oscillator system.\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 2","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01783-2.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01783-2","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We study a Hermitian matrix model with a kinetic term given by \( Tr (H \Phi ^2 )\), where H is a positive definite Hermitian matrix, similar as in the Kontsevich Matrix model, but with its potential \(\Phi ^3\) replaced by \(\Phi ^4\). We show that its partition function solves an integrable Schrödinger-type equation for a non-interacting N-body Harmonic oscillator system.
期刊介绍：
The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.
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