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The generalized hole argument is motivated and extended from the spacetime hole arguments which" /> <meta name="twitter:image" content="http://a.academia-assets.com/images/twitter-card.jpeg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/27921636/Gauges_Holes_and_their_Connections" /> <meta property="og:title" content="Gauges, Holes, and their `Connections" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="The purpose of this paper is to present a generalized hole argument for gauge field theories and their geometrical setting in terms of fiber bundles. 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The generalized hole argument is motivated and extended from the spacetime hole arguments which" /> <title>(PDF) Gauges, Holes, and their `Connections</title> <link rel="canonical" href="https://www.academia.edu/27921636/Gauges_Holes_and_their_Connections" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '129f474dbcc8e505390b0f49472dac75fb69884e'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1740154562000); window.Aedu.timeDifference = new Date().getTime() - 1740154562000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"The purpose of this paper is to present a generalized hole argument for gauge field theories and their geometrical setting in terms of fiber bundles. The generalized hole argument is motivated and extended from the spacetime hole arguments which appear in spacetime theories based on differentiable manifolds such as general relativity. Analogously, the generalized hole argument rules out fiber bundle","author":[{"@context":"https://schema.org","@type":"Person","name":"Holger Lyre","url":"https://ovgu.academia.edu/HolgerLyre"}],"contributor":[],"dateCreated":"2016-08-21","dateModified":"2016-08-21","datePublished":"1999-01-01","headline":"Gauges, Holes, and their `Connections","image":"https://attachments.academia-assets.com/48216747/thumbnails/1.jpg","inLanguage":"en","keywords":["Quantum Physics","General Relativity","Quantum Cosmology","Gauge Field Theory"],"publisher":{"@context":"https://schema.org","@type":"Organization","name":null},"sourceOrganization":[{"@context":"https://schema.org","@type":"EducationalOrganization","name":"ovgu"}],"thumbnailUrl":"https://attachments.academia-assets.com/48216747/thumbnails/1.jpg","url":"https://www.academia.edu/27921636/Gauges_Holes_and_their_Connections"}</script><style type="text/css">@media(max-width: 567px){:root{--token-mode: Rebrand;--dropshadow: 0 2px 4px 0 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{"work":{"id":27921636,"created_at":"2016-08-21T05:04:09.335-07:00","from_world_paper_id":156767864,"updated_at":"2021-01-13T11:24:46.118-08:00","_data":{"abstract":"The purpose of this paper is to present a generalized hole argument for gauge field theories and their geometrical setting in terms of fiber bundles. The generalized hole argument is motivated and extended from the spacetime hole arguments which appear in spacetime theories based on differentiable manifolds such as general relativity. Analogously, the generalized hole argument rules out fiber bundle","publication_date":"1999,,"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Gauges, Holes, and their `Connections","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [8640272]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":48216747,"attachmentType":"pdf"}"><img alt="First page of “Gauges, Holes, and their `Connections”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/48216747/mini_magick20190204-28077-3y12dk.png?1549323284" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Gauges, Holes, and their `Connections</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="8640272" href="https://ovgu.academia.edu/HolgerLyre"><img alt="Profile image of Holger Lyre" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Holger Lyre</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1999</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">13 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 27921636; const worksViewsPath = "/v0/works/views?subdomain_param=api&work_ids%5B%5D=27921636"; const getWorkViews = async (workId) => { const response = await fetch(worksViewsPath); if (!response.ok) { throw new Error('Failed to load work views'); } const data = await response.json(); return data.views[workId]; }; // Get the view count for the work - we send this immediately rather than waiting for // the DOM to load, so it can be available as soon as possible (but without holding up // the backend or other resource requests, because it's a bit expensive and not critical). const viewCount = await getWorkViews(workId); const updateViewCount = (viewCount) => { try { const viewCountNumber = parseInt(viewCount, 10); if (viewCountNumber === 0) { // Remove the whole views element if there are zero views. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); return; } const commaizedViewCount = viewCountNumber.toLocaleString(); const viewCountBody = document.getElementById('work-metadata-view-count'); if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">The purpose of this paper is to present a generalized hole argument for gauge field theories and their geometrical setting in terms of fiber bundles. The generalized hole argument is motivated and extended from the spacetime hole arguments which appear in spacetime theories based on differentiable manifolds such as general relativity. Analogously, the generalized hole argument rules out fiber bundle</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":48216747,"attachmentType":"pdf","workUrl":"https://www.academia.edu/27921636/Gauges_Holes_and_their_Connections"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":48216747,"attachmentType":"pdf","workUrl":"https://www.academia.edu/27921636/Gauges_Holes_and_their_Connections"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions, alternative notations and jargon, and relevant facts and theorems. Special attention is given to detailed figures and geometric viewpoints, some of which would seem to be novel to the literature. Topics are avoided which are well covered in textbooks, such as historical motivations, proofs and derivations, and tools for practical calculations. The present paper is best read in conjunction with the similar paper on Riemannian geometry cited herein.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Gauge Theories and Fiber Bundles: Definitions, Pictures, and Results","attachmentId":76100720,"attachmentType":"pdf","work_url":"https://www.academia.edu/63797283/Gauge_Theories_and_Fiber_Bundles_Definitions_Pictures_and_Results","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/63797283/Gauge_Theories_and_Fiber_Bundles_Definitions_Pictures_and_Results"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="109385042" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/109385042/The_Hole_Argument_and_Beyond_Part_II_Treating_Non_isomorphic_Spacetimes">The Hole Argument and Beyond, Part II: Treating Non-isomorphic Spacetimes</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="235656" href="https://cambridge.academia.edu/JeremyButterfield">Jeremy Butterfield</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2023</p><p class="ds-related-work--abstract ds2-5-body-sm">In this two-part paper we review, and then develop, the assessment of the hole argument for general relativity. The review (in Part I) discussed how to compare points in isomorphic spacetimes, i.e. models of the theory. This second Part proposes a framework for making comparisons of non-isomorphic spacetimes. It combines two ideas we discussed in Part I-the philosophical idea of counterparts, and the idea of threading points between spacetimes other than by isomorphism-with the mathematics of fibre bundles. We first recall the ideas from Part I (Section 1). Then in Section 2 and an Appendix, we define a fibre bundle whose fibres are isomorphic copies of a given spacetime or model, and discuss connections on this fibre bundle. This material proceeds on analogy with field-space formulations of gauge theories. Finally, in Section 3, we show how this fibre bundle gives natural expressions of the philosophical ideas of counterparts, and of threading.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Hole Argument and Beyond, Part II: Treating Non-isomorphic Spacetimes","attachmentId":107526629,"attachmentType":"pdf","work_url":"https://www.academia.edu/109385042/The_Hole_Argument_and_Beyond_Part_II_Treating_Non_isomorphic_Spacetimes","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/109385042/The_Hole_Argument_and_Beyond_Part_II_Treating_Non_isomorphic_Spacetimes"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="57978450" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/57978450/The_hole_argument_for_covariant_theories">The hole argument for covariant theories</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33065408" href="https://bu.academia.edu/JohnStachel">John Stachel</a></div><p class="ds-related-work--metadata ds2-5-body-xs">General Relativity and Gravitation, 2006</p><p class="ds-related-work--abstract ds2-5-body-sm">The hole argument was developed by Einstein in 1913 while he was searching for a relativistic theory of gravitation. Einstein used the language of coordinate systems and coordinate invariance, rather than the language of manifolds and diffeomorphism invariance. He formulated the hole argument against covariant field equations and later found a way to avoid it using coordinate language. In this paper we shall use the invariant language of categories, manifolds and natural objects to give a coordinate-free description of the hole argument and a way of avoiding it. Finally we shall point out some important implications of further extensions of the hole argument to sets and relations for the problem of quantum gravity.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The hole argument for covariant theories","attachmentId":72613628,"attachmentType":"pdf","work_url":"https://www.academia.edu/57978450/The_hole_argument_for_covariant_theories","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/57978450/The_hole_argument_for_covariant_theories"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="9269102" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/9269102/Fiber_Bundles_Yang_Mills_Theory_and_General_Relativity">Fiber Bundles, Yang-Mills Theory, and General Relativity</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="48108" href="https://uci.academia.edu/JamesOwenWeatherall">James Owen Weatherall</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Synthese</p><p class="ds-related-work--abstract ds2-5-body-sm">I articulate and discuss a geometrical interpretation of Yang-Mills theory. Analogies and disanalogies between Yang-Mills theory and general relativity are also considered.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fiber Bundles, Yang-Mills Theory, and General Relativity","attachmentId":37745847,"attachmentType":"pdf","work_url":"https://www.academia.edu/9269102/Fiber_Bundles_Yang_Mills_Theory_and_General_Relativity","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/9269102/Fiber_Bundles_Yang_Mills_Theory_and_General_Relativity"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="27921637" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/27921637/Fiber_Bundle_Gauge_Theories_and_Fields_Dilemma">Fiber Bundle Gauge Theories and "Field's Dilemma</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="8640272" href="https://ovgu.academia.edu/HolgerLyre">Holger Lyre</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2000</p><p class="ds-related-work--abstract ds2-5-body-sm">We propose a distinction between the physical and the mathematical parts of gauge field theories. The main problem we face is to uphold a strong and meaningful criterion of what is physical. We like to call it &quot;Field&#39;s dilemma&quot;, referring to Hartry Field&#39;s nominalist proposal which we consider to be inadaequate. The resolution to the dilemma, we believe, is implicitly</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fiber Bundle Gauge Theories and \"Field's Dilemma","attachmentId":48216748,"attachmentType":"pdf","work_url":"https://www.academia.edu/27921637/Fiber_Bundle_Gauge_Theories_and_Fields_Dilemma","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/27921637/Fiber_Bundle_Gauge_Theories_and_Fields_Dilemma"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="42127207" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/42127207/THEORY_OF_NATURAL_BUNDLES_AND_GAUGE_FIELDS">THEORY OF NATURAL BUNDLES AND GAUGE FIELDS</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7036490" href="https://204.academia.edu/ZafarTurakulov">Zafar Turakulov</a></div><p class="ds-related-work--abstract ds2-5-body-sm">An explicit model of fiber bundle with local fibers being distinct copies of isotopic space is introduced. The local isotopic spaces are endowed with frames which are used as local isotopic ones. The field local of isotopic frames are considered as gauge field itself while the form of gauge connections is derived from it. The field equation for that of local frames is found. It is shown that Yang-Mills equation follows from it, but variety of solutions of the new equation is highly reduced such that no ambiguities (Yang-Wu and vacuum ones) arise. It is shown that Lagrangian for the field gives non-zero trace for the stress-energy tensor and zero value for the field of plane wave. New solutions for the fields of punctual source and spherical wave are found.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"THEORY OF NATURAL BUNDLES AND GAUGE FIELDS","attachmentId":62262102,"attachmentType":"pdf","work_url":"https://www.academia.edu/42127207/THEORY_OF_NATURAL_BUNDLES_AND_GAUGE_FIELDS","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/42127207/THEORY_OF_NATURAL_BUNDLES_AND_GAUGE_FIELDS"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="125428687" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/125428687/Multi_Fibers_Bundles_as_a_new_model_for_high_dimensional_Spacetimes">Multi-Fibers Bundles as a new model for high-dimensional Spacetimes</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="323122585" href="https://independent.academia.edu/StephaneCollion">Stephane Collion</a></div><p class="ds-related-work--metadata ds2-5-body-xs">arXiv (Cornell University), 2017</p><p class="ds-related-work--abstract ds2-5-body-sm">Around 1920, Kaluza and Klein had the idea to add a fifth dimension to the classical 4-dimensional spacetime of general relativity to create a geometric theory of gravitation and electromagnetism. Today, theoretical evidences, like string theory, suggest the need for a spacetime with more than five dimensions. The mathematical translation of the heuristic idea of a 4-dimensional classical spacetime equipped with extra "small" dimensions, is a fiber bundle structure π : M → M on a (4 + k)-dimensional manifold M , with fiber a compact manifold F of dimension k, more shortly a F -fibration. Kaluza and Klein used a fibration with fiber the standard circle S 1 , this fiber carrying the electromagnetic potential. Inclusion of other physical interaction would therefore require a F -fibration with F of the form F = S 1 × W , W being a compact manifold. However, with such a F -fibration, they is no naturally defined fiber diffeomorphic to S 1 at each point of the manifold, and therefore one looses the possibility to define simply the electromagnetic potential. We want to present in this paper a mathematical structure generalizing the fiber bundle, that enable the possible definition of multiple naturally defined fibers at each point of the manifold, on which therefore one can define objects that depend only on one of the components, S 1 or W , of the global (S 1 × W ) fiber. Although we do not pretend here to model precisely other known physical interactions, we present this geometric structure as a possible way to model or encode deviations from standard 4-dimensional General Relativity, or "dark" effects such as dark matter or energy ; (we refer to the authors' article from which this paper is extracted, but whose purpose is different). Also this geometry was a starting point for the second author's new approach to a geometric unification of General Relativity and Quantum Physics ( see ). 1 Full details of this use of the multi-fibers structure can be found in [3] : S. Collion, M. Vaugon, A New Approach to Kaluza-Klein theory. arXiv.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Multi-Fibers Bundles as a new model for high-dimensional Spacetimes","attachmentId":119473777,"attachmentType":"pdf","work_url":"https://www.academia.edu/125428687/Multi_Fibers_Bundles_as_a_new_model_for_high_dimensional_Spacetimes","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/125428687/Multi_Fibers_Bundles_as_a_new_model_for_high_dimensional_Spacetimes"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="92715225" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/92715225/Extended_Gauge_Principle_and_Quantization_of_Gauge_Theories">Extended Gauge Principle and Quantization of Gauge Theories</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="149267844" href="https://independent.academia.edu/JorgeAndr%C3%A9sDevoto">Jorge Andrés Devoto</a></div><p class="ds-related-work--metadata ds2-5-body-xs">AIP Conference Proceedings, 2006</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Extended Gauge Principle and Quantization of Gauge Theories","attachmentId":95651022,"attachmentType":"pdf","work_url":"https://www.academia.edu/92715225/Extended_Gauge_Principle_and_Quantization_of_Gauge_Theories","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/92715225/Extended_Gauge_Principle_and_Quantization_of_Gauge_Theories"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="30437517" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/30437517/The_action_of_the_group_of_bundle_automorphisms_on_the_space_of_connections_and_the_geometry_of_gauge_theories">The action of the group of bundle-automorphisms on the space of connections and the geometry of gauge theories</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="57886487" href="https://sissa.academia.edu/cesarereina">cesare reina</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Geometry and Physics, 1984</p><p class="ds-related-work--abstract ds2-5-body-sm">Some aspects of the geometry of gauge theories are sketched in this review. We deal essentially with Yang-Mills theory, discussing the structure of the space of gauge orbits and the geometrical interpretation of ghosts and anomalies. Occasionally we deal also with classical egauge theories, of gravitation and in particular we study the action of the group of diffeomorphisms on the space of linear connections. Finally we comment on the mathematical interpretation of anomalies in field theories.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The action of the group of bundle-automorphisms on the space of connections and the geometry of gauge theories","attachmentId":50879984,"attachmentType":"pdf","work_url":"https://www.academia.edu/30437517/The_action_of_the_group_of_bundle_automorphisms_on_the_space_of_connections_and_the_geometry_of_gauge_theories","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/30437517/The_action_of_the_group_of_bundle_automorphisms_on_the_space_of_connections_and_the_geometry_of_gauge_theories"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="8218899" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/8218899/Enlarged_geometries_of_gauge_bundles">Enlarged geometries of gauge bundles</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="16073598" href="https://independent.academia.edu/AnaLuciaBarbosa">Ana-Lucia Barbosa</a></div><p class="ds-related-work--abstract ds2-5-body-sm">The geometrical picture of gauge theories must be enlarged when a gauge potential ceases to behave like a connection, as it does in electroweak interactions. When the gauge group has dimension four, the vector space isomorphism between spacetime and the gauge algebra is realized by a tetradlike field. The object measuring the deviation from a strict bundle structure has the formal behavior of a spacetime connection, of which the deformed gauge field-strength is the torsion. A generalized derivative emerges in terms of which the two Bianchi identities are formally recovered. Effects of gravitational type turn up. The dynamical equations obtained correspond to a broken gauge model on a curved spacetime.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Enlarged geometries of gauge bundles","attachmentId":34645418,"attachmentType":"pdf","work_url":"https://www.academia.edu/8218899/Enlarged_geometries_of_gauge_bundles","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/8218899/Enlarged_geometries_of_gauge_bundles"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":48216747,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":48216747,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_48216747" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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