{"title":"A Bekenstein-Type Bound in QFT","authors":"Roberto Longo","doi":"10.1007/s00220-025-05261-1","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>B</i> be a spacetime region of width <span>\\(2R >0\\)</span>, and <span>\\(\\varphi \\)</span> a vector state localized in <i>B</i>. We show that the vacuum relative entropy of <span>\\(\\varphi \\)</span>, on the local von Neumann algebra of <i>B</i>, is bounded by <span>\\(2\\pi R\\)</span>-times the energy of the state <span>\\(\\varphi \\)</span> in <i>B</i>. This bound is model-independent and rigorous; it follows solely from first principles in the framework of translation covariant, local Quantum Field Theory on the Minkowski spacetime.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 5","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-025-05261-1.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00220-025-05261-1","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Let B be a spacetime region of width \(2R >0\), and \(\varphi \) a vector state localized in B. We show that the vacuum relative entropy of \(\varphi \), on the local von Neumann algebra of B, is bounded by \(2\pi R\)-times the energy of the state \(\varphi \) in B. This bound is model-independent and rigorous; it follows solely from first principles in the framework of translation covariant, local Quantum Field Theory on the Minkowski spacetime.
期刊介绍:
The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.