图上的量子大地流

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Letters in Mathematical Physics Pub Date : 2024-09-16 DOI:10.1007/s11005-024-01860-6

Edwin Beggs, Shahn Majid

{"title":"图上的量子大地流","authors":"Edwin Beggs, Shahn Majid","doi":"10.1007/s11005-024-01860-6","DOIUrl":null,"url":null,"abstract":"<div>We revisit the construction of quantum Riemannian geometries on graphs starting from a hermitian metric compatible connection, which always exists. We use this method to find quantum Levi-Civita connections on the n-leg star graph for \\(n=2,3,4\\) and find the same phenomenon as recently found for the \\(A_n\\) Dynkin graph that the metric length for each inbound arrow has to exceed the length in the other direction by a multiple, here \\(\\sqrt{n}\\). We then study quantum geodesics on graphs and construct these on the 4-leg graph and on the integer lattice line \\(\\mathbb {Z}\\) with a general edge-symmetric metric.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01860-6.pdf","citationCount":"0","resultStr":"{\"title\":\"Quantum geodesic flows on graphs\",\"authors\":\"Edwin Beggs, Shahn Majid\",\"doi\":\"10.1007/s11005-024-01860-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>We revisit the construction of quantum Riemannian geometries on graphs starting from a hermitian metric compatible connection, which always exists. We use this method to find quantum Levi-Civita connections on the n-leg star graph for \\\\(n=2,3,4\\\\) and find the same phenomenon as recently found for the \\\\(A_n\\\\) Dynkin graph that the metric length for each inbound arrow has to exceed the length in the other direction by a multiple, here \\\\(\\\\sqrt{n}\\\\). We then study quantum geodesics on graphs and construct these on the 4-leg graph and on the integer lattice line \\\\(\\\\mathbb {Z}\\\\) with a general edge-symmetric metric.</div>\",\"PeriodicalId\":685,\"journal\":{\"name\":\"Letters in Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11005-024-01860-6.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Letters in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11005-024-01860-6\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-024-01860-6","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

摘要

我们重温了在图上构建量子黎曼几何图形的方法，它是从一个始终存在的与赫米提度量兼容的连接开始的。我们用这种方法找到了 \(n=2,3,4\) n 脚星形图上的量子列维-奇维塔连接，并发现了最近在 \(A_n\) Dynkin 图上发现的相同现象，即每个向内箭头的度量长度必须超过另一方向长度的倍数，这里是 \(\sqrt{n}\)。然后，我们研究图上的量子测地线，并在 4 脚图上和具有一般边对称度量的整数网格线 \(\mathbb {Z}\) 上构建量子测地线。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Quantum geodesic flows on graphs

查看原文本刊更多论文

Quantum geodesic flows on graphs

We revisit the construction of quantum Riemannian geometries on graphs starting from a hermitian metric compatible connection, which always exists. We use this method to find quantum Levi-Civita connections on the n-leg star graph for \(n=2,3,4\) and find the same phenomenon as recently found for the \(A_n\) Dynkin graph that the metric length for each inbound arrow has to exceed the length in the other direction by a multiple, here \(\sqrt{n}\). We then study quantum geodesics on graphs and construct these on the 4-leg graph and on the integer lattice line \(\mathbb {Z}\) with a general edge-symmetric metric.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

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.