T2×R上均匀通量背景下的无质量费米子：使用晶格调节器的单粒子填充模式的真空量子数

IF 5 2区物理与天体物理 Q1 Physics and Astronomy

Physical Review D Pub Date : 2025-01-10 DOI:10.1103/physrevd.111.014502

Nikhil Karthik, Rajamani Narayanan, Ray Romero

{"title":"T2×R上均匀通量背景下的无质量费米子：使用晶格调节器的单粒子填充模式的真空量子数","authors":"Nikhil Karthik, Rajamani Narayanan, Ray Romero","doi":"10.1103/physrevd.111.014502","DOIUrl":null,"url":null,"abstract":"The quantum numbers of monopoles in R</a:mi></a:mrow>3</a:mn></a:mrow></a:msup></a:mrow></a:math> in the presence of massless fermions have been analyzed using a uniform flux background in <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><c:msup><c:mi>S</c:mi><c:mn>2</c:mn></c:msup><c:mo>×</c:mo><c:mi>R</c:mi></c:math> coupled to fermions. An analogous study in <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><e:msup><e:mi>T</e:mi><e:mn>2</e:mn></e:msup><e:mo>×</e:mo><e:mi>R</e:mi></e:math> is performed by studying the discrete symmetries of the Dirac Hamiltonian in the presence of a static uniform field on <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><g:msup><g:mi>T</g:mi><g:mn>2</g:mn></g:msup></g:math> with a total flux of <i:math xmlns:i=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><i:mi>Q</i:mi></i:math> in the continuum. The degenerate ground states are classified based on their transformation properties under <k:math xmlns:k=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><k:mfrac><k:mi>π</k:mi><k:mn>2</k:mn></k:mfrac></k:math> rotations of <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><m:msup><m:mi>T</m:mi><m:mn>2</m:mn></m:msup></m:math> that leave the background field invariant. We find that the lattice analysis with overlap fermions exactly reproduces the transformation properties of the single-particle zero modes in the continuum. Whereas the transformation properties of the single-particle negative energy states can be studied in the continuum and the lattice, we are also able to study the transformation properties and the particle number (charge) of the many-body ground state on a finite lattice, and we show that the contributions from the fully filled single-particle states cannot be ignored. Published by the American Physical Society 2025 ","PeriodicalId":20167,"journal":{"name":"Physical Review D","volume":"46 1","pages":""},"PeriodicalIF":5.0000,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Massless fermions in uniform flux background on T2×R : Vacuum quantum numbers from single-particle filled modes using lattice regulator\",\"authors\":\"Nikhil Karthik, Rajamani Narayanan, Ray Romero\",\"doi\":\"10.1103/physrevd.111.014502\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The quantum numbers of monopoles in R</a:mi></a:mrow>3</a:mn></a:mrow></a:msup></a:mrow></a:math> in the presence of massless fermions have been analyzed using a uniform flux background in <c:math xmlns:c=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><c:msup><c:mi>S</c:mi><c:mn>2</c:mn></c:msup><c:mo>×</c:mo><c:mi>R</c:mi></c:math> coupled to fermions. An analogous study in <e:math xmlns:e=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><e:msup><e:mi>T</e:mi><e:mn>2</e:mn></e:msup><e:mo>×</e:mo><e:mi>R</e:mi></e:math> is performed by studying the discrete symmetries of the Dirac Hamiltonian in the presence of a static uniform field on <g:math xmlns:g=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><g:msup><g:mi>T</g:mi><g:mn>2</g:mn></g:msup></g:math> with a total flux of <i:math xmlns:i=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><i:mi>Q</i:mi></i:math> in the continuum. The degenerate ground states are classified based on their transformation properties under <k:math xmlns:k=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><k:mfrac><k:mi>π</k:mi><k:mn>2</k:mn></k:mfrac></k:math> rotations of <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><m:msup><m:mi>T</m:mi><m:mn>2</m:mn></m:msup></m:math> that leave the background field invariant. We find that the lattice analysis with overlap fermions exactly reproduces the transformation properties of the single-particle zero modes in the continuum. Whereas the transformation properties of the single-particle negative energy states can be studied in the continuum and the lattice, we are also able to study the transformation properties and the particle number (charge) of the many-body ground state on a finite lattice, and we show that the contributions from the fully filled single-particle states cannot be ignored. Published by the American Physical Society 2025 \",\"PeriodicalId\":20167,\"journal\":{\"name\":\"Physical Review D\",\"volume\":\"46 1\",\"pages\":\"\"},\"PeriodicalIF\":5.0000,\"publicationDate\":\"2025-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review D\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevd.111.014502\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review D","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevd.111.014502","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}

引用次数: 0

摘要

利用S2×R中与费米子耦合的均匀通量背景，分析了无质量费米子存在下R3中单极子的量子数。在T2×R中进行了一个类似的研究，研究了在连续统中总通量为Q的T2上存在静态均匀场时狄拉克哈密顿量的离散对称性。根据简并基态在T2的π - 2旋转下保持背景场不变的变换性质对它们进行分类。我们发现重叠费米子的晶格分析准确地再现了连续介质中单粒子零模的变换特性。单粒子负能态的转换性质可以在连续介质和晶格中研究，我们也可以在有限晶格中研究多体基态的转换性质和粒子数（电荷），并证明了完全填充的单粒子态的贡献是不可忽视的。2025年由美国物理学会出版

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Massless fermions in uniform flux background on T2×R : Vacuum quantum numbers from single-particle filled modes using lattice regulator

The quantum numbers of monopoles in R3 in the presence of massless fermions have been analyzed using a uniform flux background in S2×R coupled to fermions. An analogous study in T2×R is performed by studying the discrete symmetries of the Dirac Hamiltonian in the presence of a static uniform field on T2 with a total flux of Q in the continuum. The degenerate ground states are classified based on their transformation properties under π2 rotations of T2 that leave the background field invariant. We find that the lattice analysis with overlap fermions exactly reproduces the transformation properties of the single-particle zero modes in the continuum. Whereas the transformation properties of the single-particle negative energy states can be studied in the continuum and the lattice, we are also able to study the transformation properties and the particle number (charge) of the many-body ground state on a finite lattice, and we show that the contributions from the fully filled single-particle states cannot be ignored.

Published by the American Physical Society

2025

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

Physical Review D 物理-天文与天体物理

CiteScore

9.20

自引率

36.00%

发文量

审稿时长

2 months

期刊介绍： Physical Review D (PRD) is a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics. PRD covers experimental and theoretical results in all aspects of particle physics, field theory, gravitation and cosmology, including: Particle physics experiments, Electroweak interactions, Strong interactions, Lattice field theories, lattice QCD, Beyond the standard model physics, Phenomenological aspects of field theory, general methods, Gravity, cosmology, cosmic rays, Astrophysics and astroparticle physics, General relativity, Formal aspects of field theory, field theory in curved space, String theory, quantum gravity, gauge/gravity duality.