{"title":"Moyal product and generalized Hom-Lie-Virasoro symmetries in Bloch electron systems","authors":"","doi":"10.1016/j.nuclphysb.2024.116639","DOIUrl":null,"url":null,"abstract":"<div><p>We explore two variations of the Curtright-Zachos (CZ) deformation of the Virasoro algebra. Firstly, we introduce a scaled CZ algebra that inherits the scaling structure found in the differential operator representation of the magnetic translation (MT) operators. We then linearly decompose the scaled CZ generators to derive two types of Hom-Lie deformations of the <span><math><msub><mrow><mi>W</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> algebra. We discuss ⁎-bracket formulations of these algebras and their connection to the Moyal product. We show that the ⁎-bracket form of the scaled CZ algebra arises from the Moyal product, while we obtain the second type of deformed <span><math><msub><mrow><mi>W</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> through a coordinate transformation of the first type of Moyal operators. From a physical point of view, we construct the Hamiltonian of a tight binding model (TBM) using the Wyle matrix representation of the scaled CZ algebra. We note that the integer powers of <em>q</em> are linked to the quantum fluctuations that are inherent in the Moyal product.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0550321324002050/pdfft?md5=9a38b9255b03882387f94818cb0ee3cc&pid=1-s2.0-S0550321324002050-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Physics B","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0550321324002050","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 0
Abstract
We explore two variations of the Curtright-Zachos (CZ) deformation of the Virasoro algebra. Firstly, we introduce a scaled CZ algebra that inherits the scaling structure found in the differential operator representation of the magnetic translation (MT) operators. We then linearly decompose the scaled CZ generators to derive two types of Hom-Lie deformations of the algebra. We discuss ⁎-bracket formulations of these algebras and their connection to the Moyal product. We show that the ⁎-bracket form of the scaled CZ algebra arises from the Moyal product, while we obtain the second type of deformed through a coordinate transformation of the first type of Moyal operators. From a physical point of view, we construct the Hamiltonian of a tight binding model (TBM) using the Wyle matrix representation of the scaled CZ algebra. We note that the integer powers of q are linked to the quantum fluctuations that are inherent in the Moyal product.
期刊介绍:
Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.