{"title":"利用克利福德代数方程求解杨-巴克斯特方程、四面体方程和高次单纯形方程","authors":"","doi":"10.1016/j.nuclphysb.2024.116664","DOIUrl":null,"url":null,"abstract":"<div><p>Bethe Ansatz was discovered in 1932. Half a century later its algebraic structure was unearthed: Yang-Baxter equation was discovered, as well as its multidimensional generalizations [tetrahedron equation and <em>d</em>-simplex equations]. Here we describe a universal method to solve these equations using Clifford algebras. The Yang-Baxter equation (<span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span>), Zamolodchikov's tetrahedron equation (<span><math><mi>d</mi><mo>=</mo><mn>3</mn></math></span>) and the Bazhanov-Stroganov equation (<span><math><mi>d</mi><mo>=</mo><mn>4</mn></math></span>) are special cases. Our solutions form a linear space. This helps us to include spectral parameters. Potential applications are discussed.</p></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S055032132400230X/pdfft?md5=cacf76f9191ead08813e1b3c4b155908&pid=1-s2.0-S055032132400230X-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras\",\"authors\":\"\",\"doi\":\"10.1016/j.nuclphysb.2024.116664\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Bethe Ansatz was discovered in 1932. Half a century later its algebraic structure was unearthed: Yang-Baxter equation was discovered, as well as its multidimensional generalizations [tetrahedron equation and <em>d</em>-simplex equations]. Here we describe a universal method to solve these equations using Clifford algebras. The Yang-Baxter equation (<span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span>), Zamolodchikov's tetrahedron equation (<span><math><mi>d</mi><mo>=</mo><mn>3</mn></math></span>) and the Bazhanov-Stroganov equation (<span><math><mi>d</mi><mo>=</mo><mn>4</mn></math></span>) are special cases. Our solutions form a linear space. This helps us to include spectral parameters. Potential applications are discussed.</p></div>\",\"PeriodicalId\":54712,\"journal\":{\"name\":\"Nuclear Physics B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-09-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S055032132400230X/pdfft?md5=cacf76f9191ead08813e1b3c4b155908&pid=1-s2.0-S055032132400230X-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nuclear Physics B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S055032132400230X\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Physics B","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S055032132400230X","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}
Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras
Bethe Ansatz was discovered in 1932. Half a century later its algebraic structure was unearthed: Yang-Baxter equation was discovered, as well as its multidimensional generalizations [tetrahedron equation and d-simplex equations]. Here we describe a universal method to solve these equations using Clifford algebras. The Yang-Baxter equation (), Zamolodchikov's tetrahedron equation () and the Bazhanov-Stroganov equation () are special cases. Our solutions form a linear space. This helps us to include spectral parameters. Potential applications are discussed.
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.