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In other words, there" /> <meta name="twitter:image" content="https://0.academia-photos.com/631545/218015/254671/s200_francisco.doria.jpg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/1405622/The_geometry_of_gauge_field_copies" /> <meta property="og:title" content="The geometry of gauge field copies" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="We show that a gauge field uniquely determines its potential if and only if its holonomy group coincides with the gauge group on every open set in spacetime, provided that the field is not degenerate as a 2-form over spacetime. 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{"work":{"id":1405622,"created_at":"2012-02-17T18:28:34.905-08:00","from_world_paper_id":35398006,"updated_at":"2025-02-01T20:12:34.955-08:00","_data":{"publisher":"Springer","ai_title_tag":"Gauge Fields and Their Potential Uniqueness","grobid_abstract":"We show that a gauge field uniquely determines its potential if and only if its holonomy group coincides with the gauge group on every open set in spacetime, provided that the field is not degenerate as a 2-form over spacetime. In other words, there is no potential ambiguity whenever such a field is irreducible everywhere in spacetime. We then show that the ambiguous potentials for those gauge fields are partitioned into gauge-equivalence classes (modulo certain homotopy classes) as a consequence of the nontrivial connectivity of spacetime. These homotopy classes depend on the gauge group, on the holonomy group and on this last group's centralizer in the gauge group.","publication_date":"1981,1,1","publication_name":"Communications in Mathematical Physics","grobid_abstract_attachment_id":"50984764"},"document_type":"paper","pre_hit_view_count_baseline":0,"quality":"high","language":"en","title":"The geometry of gauge field copies","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [631545]; 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":50984764,"attachmentType":"pdf"}"><img alt="First page of “The geometry of gauge field copies”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/50984764/mini_magick20190126-29246-1vutlo8.png?1548562159" /><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">The geometry of gauge field copies</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="631545" href="https://ufrj.academia.edu/FranciscoDoria"><img alt="Profile image of Francisco Antonio Doria" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/631545/218015/254671/s65_francisco.doria.jpg" />Francisco Antonio Doria</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">1981, Communications in Mathematical Physics</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">23 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 = 1405622; 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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">We show that a gauge field uniquely determines its potential if and only if its holonomy group coincides with the gauge group on every open set in spacetime, provided that the field is not degenerate as a 2-form over spacetime. In other words, there is no potential ambiguity whenever such a field is irreducible everywhere in spacetime. We then show that the ambiguous potentials for those gauge fields are partitioned into gauge-equivalence classes (modulo certain homotopy classes) as a consequence of the nontrivial connectivity of spacetime. 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Part II: A compendium of similarities between gauge transformations and diffeomorphisms","attachmentId":86067488,"attachmentType":"pdf","work_url":"https://www.academia.edu/79309019/Same_Diff_Part_II_A_compendium_of_similarities_between_gauge_transformations_and_diffeomorphisms","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/79309019/Same_Diff_Part_II_A_compendium_of_similarities_between_gauge_transformations_and_diffeomorphisms"><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="103890106" 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/103890106/Unification_mechanism_for_gauge_and_spacetime_symmetries">Unification mechanism for gauge and spacetime symmetries</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="269801881" href="https://independent.academia.edu/Andr%C3%A1sL%C3%A1szl%C3%B37">András László</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Physics A: Mathematical and Theoretical, 2017</p><p class="ds-related-work--abstract ds2-5-body-sm">A group theoretical mechanism for unification of local gauge and spacetime symmetries is introduced. 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The unified group, being an extension of the group of spacetime symmetries, is shown to be different than that of the conventional supersymmetry group, thus overcoming the McGlinn and Coleman-Mandula no-go theorems in a non-supersymmetric way.</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":"Unification mechanism for gauge and spacetime symmetries","attachmentId":103770305,"attachmentType":"pdf","work_url":"https://www.academia.edu/103890106/Unification_mechanism_for_gauge_and_spacetime_symmetries","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/103890106/Unification_mechanism_for_gauge_and_spacetime_symmetries"><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="62389364" 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/62389364/On_the_Natural_Gauge_Fields_of_Manifolds">On the Natural Gauge Fields of Manifolds</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="12165292" href="https://jinr.academia.edu/BijanSaha">Bijan Saha</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Modern Physics Letters A, 2000</p><p class="ds-related-work--abstract ds2-5-body-sm">The gauge symmetry inherent in the concept of manifold has been discussed. Within the scope of this symmetry the linear connection or displacement field can be considered as a natural gauge field on the manifold. The gauge-invariant equations for the displacement field have been derived. It has been shown that the energy–momentum tensor of this field conserves and hence the displacement field can be treated as one that transports energy and gravitates. To show the existence of the solutions of the field equations, we have derived the general form of the displacement field in Minkowski space–time which is invariant under rotation and space and time inversion. With this ansatz we found spherically-symmetric solutions of the equations in question.</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":"On the Natural Gauge Fields of Manifolds","attachmentId":75171349,"attachmentType":"pdf","work_url":"https://www.academia.edu/62389364/On_the_Natural_Gauge_Fields_of_Manifolds","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/62389364/On_the_Natural_Gauge_Fields_of_Manifolds"><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="53240466" 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/53240466/A_new_approach_to_gauge_fields">A new approach to 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="186268245" href="https://independent.academia.edu/MANOELITODESOUZA">MANOELITO DE SOUZA</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1998</p><p class="ds-related-work--abstract ds2-5-body-sm">A discrete field formalism exposes the physical meaning and the origins of gauge fields and of their symmetries and singularities.</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":"A new approach to gauge fields","attachmentId":70125027,"attachmentType":"pdf","work_url":"https://www.academia.edu/53240466/A_new_approach_to_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/53240466/A_new_approach_to_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="21825698" 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/21825698/Two_Questions_on_the_Geometry_of_Gauge_Fields">Two Questions on the Geometry of 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="631545" href="https://ufrj.academia.edu/FranciscoDoria">Francisco Antonio Doria</a></div><p class="ds-related-work--abstract ds2-5-body-sm">We first show that a theorem by Cartan that generalizes the Frobenius integrability theorem allows us (given certain conditions) to obtain noncurvature solutions for the differential Bianchi conditions and for higher-degree similar relations. We then prove that there is no algorithmic procedure to determine, for a reasonable restricted algebra of functions on spacetime, whether a given connection form satisfies the preceding conditions. A parallel result gives a version of G6del's first incompleteness theorem within an (axiomatized) theory of gauge fields.</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":"Two Questions on the Geometry of Gauge Fields","attachmentId":42577854,"attachmentType":"pdf","work_url":"https://www.academia.edu/21825698/Two_Questions_on_the_Geometry_of_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/21825698/Two_Questions_on_the_Geometry_of_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="7" data-entity-id="102016794" 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/102016794/A_geometrical_formulation_of_Abelian_gauge_structure_in_non_Abelian_gauge_theories_and_disconnected_gauge_group">A geometrical formulation of Abelian gauge structure in non‐Abelian gauge theories and disconnected gauge group</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="258113374" href="https://independent.academia.edu/krishnakumarsen">krishna kumar sen</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Mathematical Physics, 1994</p><p class="ds-related-work--abstract ds2-5-body-sm">II. TOPOLOGICAL ORIGIN OF FERMION NUMBER, VORTEX LINE AND NON-ABELIAN GAUGE FIELD Different quantization procedures suggest that to have quantum probability from a classical system we have to introduce classical probability in a specific geometrical setup. In a recent pape? 2270</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":"A geometrical formulation of Abelian gauge structure in non‐Abelian gauge theories and disconnected gauge group","attachmentId":102395577,"attachmentType":"pdf","work_url":"https://www.academia.edu/102016794/A_geometrical_formulation_of_Abelian_gauge_structure_in_non_Abelian_gauge_theories_and_disconnected_gauge_group","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/102016794/A_geometrical_formulation_of_Abelian_gauge_structure_in_non_Abelian_gauge_theories_and_disconnected_gauge_group"><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="15039537" 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/15039537/A_Manifestly_Gauge_Invariant_Approach_to_Quantum_Theories_of_Gauge_Fields">A Manifestly Gauge-Invariant Approach to Quantum Theories of 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="34056926" href="https://pennstate.academia.edu/AbhayAshtekar">Abhay Ashtekar</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="25777041" href="https://independent.academia.edu/MouraoJose">Jose Mourao</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1994</p><p class="ds-related-work--abstract ds2-5-body-sm">In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be extended to face these {\it kinematical} non-linearities squarely. We first present a pedagogical account of this problem and then suggest an avenue for its resolution.</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":"A Manifestly Gauge-Invariant Approach to Quantum Theories of Gauge Fields","attachmentId":38519042,"attachmentType":"pdf","work_url":"https://www.academia.edu/15039537/A_Manifestly_Gauge_Invariant_Approach_to_Quantum_Theories_of_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/15039537/A_Manifestly_Gauge_Invariant_Approach_to_Quantum_Theories_of_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="9" data-entity-id="98331778" 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/98331778/Gauge_invariant_functions_of_connections">Gauge invariant functions of connections</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="163197052" href="https://independent.academia.edu/AmbarSengupta">Ambar Sengupta</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the American Mathematical Society, 1994</p><p class="ds-related-work--abstract ds2-5-body-sm">It is shown that, for certain gauge groups, central functions of the holonomy variables do not determine connections up to gauge equivalence. It is also shown that, for a large class of compact groups, such functions do determine connections up to gauge equivalence. It is then shown that, for the latter type of gauge groups, the Euclidean quantum gauge field measure is determined by the expectation values of the Wilson loop variables (products of characters evaluated on holonomies).</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 invariant functions of connections","attachmentId":99712458,"attachmentType":"pdf","work_url":"https://www.academia.edu/98331778/Gauge_invariant_functions_of_connections","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/98331778/Gauge_invariant_functions_of_connections"><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":50984764,"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":50984764,"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_50984764" 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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