{"title":"The zeta determinant of the reduced Lorentz group localized at a representation","authors":"M. Spreafico","doi":"10.1007/s11005-025-01959-4","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce some spectral functions on the reduced Lorentz group and on its spinor group localized at an irreducible unitary representation, and we study their main analytic properties. More precisely, we consider the trace of the heat operator and the spectral zeta function of the Hodge Laplace operator on functions. We show that the localized zeta function has a regular analytic extension with simple poles, and we find a closed formula for the zeta determinant of the localized Hodge Laplace operator. We give a closed formula for the trace of the (global) heat operator and we study its expansion for small time.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 3","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-025-01959-4","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 introduce some spectral functions on the reduced Lorentz group and on its spinor group localized at an irreducible unitary representation, and we study their main analytic properties. More precisely, we consider the trace of the heat operator and the spectral zeta function of the Hodge Laplace operator on functions. We show that the localized zeta function has a regular analytic extension with simple poles, and we find a closed formula for the zeta determinant of the localized Hodge Laplace operator. We give a closed formula for the trace of the (global) heat operator and we study its expansion for small time.
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.