关于正交空间的注解

IF 1.7 4区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

International Journal of Theoretical Physics Pub Date : 2025-07-23 DOI:10.1007/s10773-025-06062-x

John Harding, Remi Salinas Schmeis

{"title":"关于正交空间的注解","authors":"John Harding, Remi Salinas Schmeis","doi":"10.1007/s10773-025-06062-x","DOIUrl":null,"url":null,"abstract":"<div><p>We provide two results. The first gives a finite graph constructed from consideration of mutually unbiased bases that occurs as a subgraph of the orthogonality space of <span>\\(\\mathbb {C}^3\\)</span> but not of that of <span>\\(\\mathbb {R}^3\\)</span>. The second is a companion result to the result of Tao and Tserunyan [9] that every countable graph occurs as an induced subgraph of the orthogonality space of a Hilbert space. We show that every finite graph occurs as an induced subgraph of the orthogonality space of a finite orthomodular lattice and that every graph occurs as an induced subgraph of the orthogonality space of some atomic orthomodular lattice.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"64 8","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Remarks on Orthogonality Spaces\",\"authors\":\"John Harding, Remi Salinas Schmeis\",\"doi\":\"10.1007/s10773-025-06062-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We provide two results. The first gives a finite graph constructed from consideration of mutually unbiased bases that occurs as a subgraph of the orthogonality space of <span>\\\\(\\\\mathbb {C}^3\\\\)</span> but not of that of <span>\\\\(\\\\mathbb {R}^3\\\\)</span>. The second is a companion result to the result of Tao and Tserunyan [9] that every countable graph occurs as an induced subgraph of the orthogonality space of a Hilbert space. We show that every finite graph occurs as an induced subgraph of the orthogonality space of a finite orthomodular lattice and that every graph occurs as an induced subgraph of the orthogonality space of some atomic orthomodular lattice.</p></div>\",\"PeriodicalId\":597,\"journal\":{\"name\":\"International Journal of Theoretical Physics\",\"volume\":\"64 8\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2025-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Theoretical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10773-025-06062-x\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10773-025-06062-x","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

摘要

我们提供了两个结果。第一部分给出了一个考虑互为无偏基的有限图，它是\(\mathbb {C}^3\)的正交空间的子图，而不是\(\mathbb {R}^3\)的正交空间的子图。第二个结论是Tao和Tserunyan[9]的结论的伴随结果，即每个可数图都是Hilbert空间的正交空间的诱导子图。我们证明了每一个有限图都是有限正交格的正交空间的诱导子图，以及每一个图都是原子正交格的正交空间的诱导子图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Remarks on Orthogonality Spaces

查看原文本刊更多论文

Remarks on Orthogonality Spaces

We provide two results. The first gives a finite graph constructed from consideration of mutually unbiased bases that occurs as a subgraph of the orthogonality space of \(\mathbb {C}^3\) but not of that of \(\mathbb {R}^3\). The second is a companion result to the result of Tao and Tserunyan [9] that every countable graph occurs as an induced subgraph of the orthogonality space of a Hilbert space. We show that every finite graph occurs as an induced subgraph of the orthogonality space of a finite orthomodular lattice and that every graph occurs as an induced subgraph of the orthogonality space of some atomic orthomodular lattice.

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

International Journal of Theoretical Physics 物理-物理：综合

CiteScore

2.50

自引率

21.40%

发文量

258

审稿时长

3.3 months

期刊介绍： International Journal of Theoretical Physics publishes original research and reviews in theoretical physics and neighboring fields. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory,as used in particle physics, and by fresh inquiry into quantum measurement theory, and other similarly fundamental areas, e.g. quantum geometry and quantum logic, etc.