{"title":"L 型无穷结构的同调转移与 BV 形式主义","authors":"James Maunder","doi":"arxiv-2408.12461","DOIUrl":null,"url":null,"abstract":"Explicit constructions for the minimal models of general and unimodular\nL-infinity algebra structures are given using the BV-formalism of mathematical\nphysics and the perturbative expansions of integrals. In particular, the\ngeneral formulas for the minimal model of an L-infinity algebra structure are\nan instance of the Homotopy Transfer Theorem and we recover the known formulas\nof the structure in terms of sums over rooted trees discussing their relation\nto Feynman diagrams.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"46 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Homotopy transfer for L-infinity structures and the BV-formalism\",\"authors\":\"James Maunder\",\"doi\":\"arxiv-2408.12461\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Explicit constructions for the minimal models of general and unimodular\\nL-infinity algebra structures are given using the BV-formalism of mathematical\\nphysics and the perturbative expansions of integrals. In particular, the\\ngeneral formulas for the minimal model of an L-infinity algebra structure are\\nan instance of the Homotopy Transfer Theorem and we recover the known formulas\\nof the structure in terms of sums over rooted trees discussing their relation\\nto Feynman diagrams.\",\"PeriodicalId\":501317,\"journal\":{\"name\":\"arXiv - MATH - Quantum Algebra\",\"volume\":\"46 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Quantum Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.12461\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Quantum Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.12461","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
利用数学物理学的 BV 形式主义和积分的微扰展开,给出了一般和单模态 L 无穷代数结构的最小模型的明确构造。特别是,L-无穷代数结构的最小模型的一般公式是同调转移定理的一个实例,我们用有根树的和恢复了已知的结构公式,并讨论了它们与费曼图的关系。
Homotopy transfer for L-infinity structures and the BV-formalism
Explicit constructions for the minimal models of general and unimodular
L-infinity algebra structures are given using the BV-formalism of mathematical
physics and the perturbative expansions of integrals. In particular, the
general formulas for the minimal model of an L-infinity algebra structure are
an instance of the Homotopy Transfer Theorem and we recover the known formulas
of the structure in terms of sums over rooted trees discussing their relation
to Feynman diagrams.