{"title":"An Algebraic Roadmap of Particle Theories","authors":"Nichol Furey","doi":"10.1002/andp.202400323","DOIUrl":null,"url":null,"abstract":"<p>An optimal algebraic framework of particle physics has a number of checkpoints to pass. As a minimum, models should <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mn>1</mn>\n <mo>⟩</mo>\n </mrow>\n <annotation>$\\langle 1 \\rangle$</annotation>\n </semantics></math> conform to the Coleman-Mandula theorem (or establish a loophole), <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mn>2</mn>\n <mo>⟩</mo>\n </mrow>\n <annotation>$\\langle 2 \\rangle$</annotation>\n </semantics></math> evade familiar fermion doubling problems, <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mn>3</mn>\n <mo>⟩</mo>\n </mrow>\n <annotation>$\\langle 3 \\rangle$</annotation>\n </semantics></math> naturally explain the Standard Model's chirality, <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mn>4</mn>\n <mo>⟩</mo>\n </mrow>\n <annotation>$\\langle 4 \\rangle$</annotation>\n </semantics></math> exclude B-L gauge symmetry at low energy, and <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mn>5</mn>\n <mo>⟩</mo>\n </mrow>\n <annotation>$\\langle 5 \\rangle$</annotation>\n </semantics></math> explain the existence of three generations. The framework introduced in ref. [1] is shown to passes checkpoints <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mn>1</mn>\n <mo>⟩</mo>\n <mo>,</mo>\n <mo>⟨</mo>\n <mn>2</mn>\n <mo>⟩</mo>\n <mo>,</mo>\n <mo>⟨</mo>\n <mn>3</mn>\n <mo>⟩</mo>\n <mo>,</mo>\n <mo>⟨</mo>\n <mn>4</mn>\n <mo>⟩</mo>\n </mrow>\n <annotation>$\\langle 1 \\rangle, \\langle 2 \\rangle, \\langle 3 \\rangle, \\langle 4 \\rangle$</annotation>\n </semantics></math>, and has yet to cross <span></span><math>\n <semantics>\n <mrow>\n <mo>⟨</mo>\n <mn>5</mn>\n <mo>⟩</mo>\n </mrow>\n <annotation>$\\langle 5 \\rangle$</annotation>\n </semantics></math>. The discussion is concluded by elucidating an unexpected appearance of spacetime symmetries.</p>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"537 4","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.202400323","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annalen der Physik","FirstCategoryId":"101","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/andp.202400323","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
An optimal algebraic framework of particle physics has a number of checkpoints to pass. As a minimum, models should conform to the Coleman-Mandula theorem (or establish a loophole), evade familiar fermion doubling problems, naturally explain the Standard Model's chirality, exclude B-L gauge symmetry at low energy, and explain the existence of three generations. The framework introduced in ref. [1] is shown to passes checkpoints , and has yet to cross . The discussion is concluded by elucidating an unexpected appearance of spacetime symmetries.
期刊介绍:
Annalen der Physik (AdP) is one of the world''s most renowned physics journals with an over 225 years'' tradition of excellence. Based on the fame of seminal papers by Einstein, Planck and many others, the journal is now tuned towards today''s most exciting findings including the annual Nobel Lectures. AdP comprises all areas of physics, with particular emphasis on important, significant and highly relevant results. Topics range from fundamental research to forefront applications including dynamic and interdisciplinary fields. The journal covers theory, simulation and experiment, e.g., but not exclusively, in condensed matter, quantum physics, photonics, materials physics, high energy, gravitation and astrophysics. It welcomes Rapid Research Letters, Original Papers, Review and Feature Articles.