{"title":"Perturbative BV-BFV formalism with homotopic renormalization: a case study","authors":"Minghao Wang, Gongwang Yan","doi":"10.1007/s11005-025-01913-4","DOIUrl":null,"url":null,"abstract":"<div><p>We report a rigorous quantization of topological quantum mechanics on <span>\\(\\mathbb {R}_{\\geqslant 0}\\)</span> and <span>\\(\\textbf{I}= [0, 1]\\)</span> in the perturbative BV-BFV formalism. Costello’s homotopic renormalization is extended and incorporated in our construction. As a consequence, we obtain an algebraic characterization of the solutions to the modified quantum master equation. In addition, BV quantization of the same model studied in previous work (Wang and Yan 2022) is derived from the BV-BFV quantization, leading to a comparison between two different frameworks in the study of quantum field theories on manifolds with boundaries.\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 2","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-02-28","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/s11005-025-01913-4","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 report a rigorous quantization of topological quantum mechanics on \(\mathbb {R}_{\geqslant 0}\) and \(\textbf{I}= [0, 1]\) in the perturbative BV-BFV formalism. Costello’s homotopic renormalization is extended and incorporated in our construction. As a consequence, we obtain an algebraic characterization of the solutions to the modified quantum master equation. In addition, BV quantization of the same model studied in previous work (Wang and Yan 2022) is derived from the BV-BFV quantization, leading to a comparison between two different frameworks in the study of quantum field theories on manifolds with boundaries.
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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