{"title":"On the thermodynamic limit of interacting fermions in the continuum","authors":"Oliver Siebert","doi":"10.1007/s11005-025-01919-y","DOIUrl":null,"url":null,"abstract":"<div><p>We study the dynamics of non-relativistic fermions in <span>\\(\\mathbb {R}^d\\)</span> interacting through a pair potential. Employing methods developed by Buchholz in the framework of resolvent algebras, we consider an extension of the CAR algebra where the dynamics acts as a group of <span>\\(*\\)</span>-automorphisms, which are continuous in time in all sectors for fixed particle numbers. In addition, we construct a <span>\\(C^*\\)</span>-dynamical system by identifying a suitable dense subalgebra. Finally, we briefly discuss how this framework could be used to construct KMS states in the future.\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 2","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01919-y.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-025-01919-y","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 the dynamics of non-relativistic fermions in \(\mathbb {R}^d\) interacting through a pair potential. Employing methods developed by Buchholz in the framework of resolvent algebras, we consider an extension of the CAR algebra where the dynamics acts as a group of \(*\)-automorphisms, which are continuous in time in all sectors for fixed particle numbers. In addition, we construct a \(C^*\)-dynamical system by identifying a suitable dense subalgebra. Finally, we briefly discuss how this framework could be used to construct KMS states in the future.
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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