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We develop further the fusion process of massless antisymmetric tensors of different ranks into a massive p-form and establish its duality properties. To illustrate the formalism we consider two situations. First the soldering mass generation mechanism is compared with the Higgs and Julia-Toulouse mechanisms for mass generation due to condensation of electric and magnetic topological defects. We show that the soldering mechanism interpolates between them for even dimensional spacetimes, in this way confirming the Higgs/Julia-Toulouse duality proposed by Quevedo and Trugenberger [1] a few years ago. Next, soldering is applied to the study of duality group classification of the massive forms. We show a dichotomy controlled by the parity of the operator defining the symplectic structure of the theory and find their explicit actions.","publication_date":"2003,,","publication_name":"Physics Letters B","grobid_abstract_attachment_id":"46568564"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"On the dimensional dependence of duality groups for massive p-forms","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [4792753]; 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":46568564,"attachmentType":"pdf"}"><img alt="First page of “On the dimensional dependence of duality groups for massive p-forms”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/46568564/mini_magick20190209-14043-1dgekru.png?1549737251" /><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">On the dimensional dependence of duality groups for massive p-forms</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="4792753" href="https://ufrj.academia.edu/ClovisWotzasek"><img alt="Profile image of Clovis Wotzasek" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/4792753/2040796/2404630/s65_clovis.wotzasek.jpg" />Clovis Wotzasek</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2003, Physics Letters B</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">16 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 = 26253145; 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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 study the soldering formalism in the context of abelian p-form theories. We develop further the fusion process of massless antisymmetric tensors of different ranks into a massive p-form and establish its duality properties. To illustrate the formalism we consider two situations. First the soldering mass generation mechanism is compared with the Higgs and Julia-Toulouse mechanisms for mass generation due to condensation of electric and magnetic topological defects. We show that the soldering mechanism interpolates between them for even dimensional spacetimes, in this way confirming the Higgs/Julia-Toulouse duality proposed by Quevedo and Trugenberger [1] a few years ago. Next, soldering is applied to the study of duality group classification of the massive forms. We show a dichotomy controlled by the parity of the operator defining the symplectic structure of the theory and find their explicit actions.</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":46568564,"attachmentType":"pdf","workUrl":"https://www.academia.edu/26253145/On_the_dimensional_dependence_of_duality_groups_for_massive_p_forms"}">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":46568564,"attachmentType":"pdf","workUrl":"https://www.academia.edu/26253145/On_the_dimensional_dependence_of_duality_groups_for_massive_p_forms"}"><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" data-impression-entity-id="26253145" data-impression-entity-type="2" data-impression-source="signup-banner"><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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Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables.</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 Geometric Approach to Massive p-form Duality","attachmentId":85353782,"attachmentType":"pdf","work_url":"https://www.academia.edu/78236432/A_Geometric_Approach_to_Massive_p_form_Duality","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/78236432/A_Geometric_Approach_to_Massive_p_form_Duality"><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="26253133" 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/26253133/Duality_symmetry_in_charged_p_form_theories">Duality symmetry in charged p-form 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="4792753" href="https://ufrj.academia.edu/ClovisWotzasek">Clovis Wotzasek</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Letters B, 2004</p><p class="ds-related-work--abstract ds2-5-body-sm">We study duality transformation and duality symmetry in the the electromagnetic-like charged p-form theories. It is shown that the dichotomic characterization of duality groups as Z2 or SO(2) remains as the only possibilities but are now present in all dimensions even and odd. This is a property defined in the symplectic sector of the theory both for massive and massless tensors. It is shown that the duality groups depend, in general, both on the ranks of the fields and on the dimension of the spacetime. We search for the physical origin of this two-fold property and show that it is traceable to the dimensional and rank dependence of the parity of certain operator (a generalized-curl) that naturally decomposes the symplectic sector of the action. These operators are only slightly different in the massive and in the massless cases but their physical origin are quite distinct.</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":"Duality symmetry in charged p-form theories","attachmentId":46568546,"attachmentType":"pdf","work_url":"https://www.academia.edu/26253133/Duality_symmetry_in_charged_p_form_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/26253133/Duality_symmetry_in_charged_p_form_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="2" data-entity-id="7989653" 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/7989653/Geometric_representation_of_the_generator_of_duality_in_massless_and_massive_p_form_field_theories">Geometric representation of the generator of duality in massless and massive p-form field 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="15269860" href="https://independent.academia.edu/LorenzoLeal">Lorenzo Leal</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review D, 2010</p><p class="ds-related-work--abstract ds2-5-body-sm">We study the invariance under duality transformations in massless and massive p−form field theories and obtain the Noether generators of the infinitesimal transformations that correspond to this symmetry. These generators are realized in geometrical representations that generalize the Loop Representation of the Maxwell field, allowing for a geometrical interpretation which is studied.</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":"Geometric representation of the generator of duality in massless and massive p-form field theories","attachmentId":48262587,"attachmentType":"pdf","work_url":"https://www.academia.edu/7989653/Geometric_representation_of_the_generator_of_duality_in_massless_and_massive_p_form_field_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/7989653/Geometric_representation_of_the_generator_of_duality_in_massless_and_massive_p_form_field_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="3987823" 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/3987823/On_the_dual_equivalence_of_the_self_dual_and_topologically_massive_p_form_models">On the dual equivalence of the self-dual and topologically massive p-form models</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="4792753" href="https://ufrj.academia.edu/ClovisWotzasek">Clovis Wotzasek</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Letters B, 2003</p><p class="ds-related-work--abstract ds2-5-body-sm">We study the duality symmetry in p-form models containing a generalized Bq∧Fp+1 term in spacetime manifolds of arbitrary dimensions. The equivalence between the Bq∧Fp+1 self-dual (SDB∧F) and the Bq∧Fp+1 topologically massive (TMB∧F) models is established using a gauge embedding procedure, including the minimal coupling to conserved charged matter current. The minimal coupling adopted for both tensor fields in the self-dual representation is transformed into a non-minimal magnetic like coupling in the topologically massive representation but with the currents swapped. It is known that to establish this equivalence a current–current interaction term is needed to render the matter sector unchanged. We show that both terms arise naturally from the embedding adopted. Comparison with Higgs/Julia–Toulouse duality is established.</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 dual equivalence of the self-dual and topologically massive p-form models","attachmentId":50095838,"attachmentType":"pdf","work_url":"https://www.academia.edu/3987823/On_the_dual_equivalence_of_the_self_dual_and_topologically_massive_p_form_models","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/3987823/On_the_dual_equivalence_of_the_self_dual_and_topologically_massive_p_form_models"><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="7989642" 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/7989642/Geometric_approach_to_a_massive_p_form_duality">Geometric approach to a massive p form duality</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="15269860" href="https://independent.academia.edu/LorenzoLeal">Lorenzo Leal</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review D, 2003</p><p class="ds-related-work--abstract ds2-5-body-sm">Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators analogous to the Wilson Loop and the 't Hooft disorder operators. Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables.</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":"Geometric approach to a massive p form duality","attachmentId":34456635,"attachmentType":"pdf","work_url":"https://www.academia.edu/7989642/Geometric_approach_to_a_massive_p_form_duality","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/7989642/Geometric_approach_to_a_massive_p_form_duality"><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="18149138" 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/18149138/Duality_self_duality_sources_and_charge_quantization_in_abelian_N_form_theories">Duality, self-duality, sources and charge quantization in abelian N-form 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="38112333" href="https://independent.academia.edu/MarcHenneaux">Marc Henneaux</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Letters B, 1997</p><p class="ds-related-work--abstract ds2-5-body-sm">We investigate duality properties of N -form fields, provide a symmetric way of coupling them to electric/magnetic sources, and check that these charges obey the appropriate quantization requirements. First, we contrast the D = 4k case, in which duality is a well-defined SO(2) rotation generated by a Chern-Simons form leaving the action invariant, and D = 4k + 2 where the corresponding ostensibly SO(1,1) rotation is not only not an invariance but does not even have a generator. When charged sources are included we show explicitly in the Maxwell case how the usual Dirac quantization arises in a fully symmetric approach attaching strings to both types of charges. Finally, for D = 4k + 2 systems, we show how charges can be introduced for self-dual (2k)-forms, and obtain the D = 4k models with sources by dimensional reduction, tracing their duality invariance to a partial invariance in the higher dimensions.</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":"Duality, self-duality, sources and charge quantization in abelian N-form theories","attachmentId":39901349,"attachmentType":"pdf","work_url":"https://www.academia.edu/18149138/Duality_self_duality_sources_and_charge_quantization_in_abelian_N_form_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/18149138/Duality_self_duality_sources_and_charge_quantization_in_abelian_N_form_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="6" data-entity-id="124537193" 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/124537193/Abelian_p_form_p_1_2_3_gauge_theories_as_the_field_theoretic_models_for_the_Hodge_theory">Abelian p-form (p = 1, 2, 3) gauge theories as the field theoretic models for the Hodge theory</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="236559795" href="https://independent.academia.edu/ROHITKUMAR4622">ROHIT KUMAR</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Modern Physics A, 2014</p><p class="ds-related-work--abstract ds2-5-body-sm">Taking the simple examples of an Abelian 1-form gauge theory in two (1+1)-dimensions, a 2-form gauge theory in four (3+1)-dimensions and a 3-form gauge theory in six (5+1)-dimensions of space–time, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = ...</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":"Abelian p-form (p = 1, 2, 3) gauge theories as the field theoretic models for the Hodge theory","attachmentId":118743492,"attachmentType":"pdf","work_url":"https://www.academia.edu/124537193/Abelian_p_form_p_1_2_3_gauge_theories_as_the_field_theoretic_models_for_the_Hodge_theory","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/124537193/Abelian_p_form_p_1_2_3_gauge_theories_as_the_field_theoretic_models_for_the_Hodge_theory"><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="127795943" 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/127795943/Duality_invariance_in_massive_theories">Duality invariance in massive 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="255045478" href="https://independent.academia.edu/DavidManuelsBenitezSierra">David Manuel's Benitez Sierra</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physical Review D, 2015</p><p class="ds-related-work--abstract ds2-5-body-sm">In this work, we show that duality symmetry can be implemented for massive theories at the level of the action, whenever we can formulate appropriates gauge invariant actions. For a massive vectorial field, we use a known gauge invariant description, while for a massive graviton, we introduce a novel gauge invariant action in order to show duality invariance.</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":"Duality invariance in massive theories","attachmentId":121476881,"attachmentType":"pdf","work_url":"https://www.academia.edu/127795943/Duality_invariance_in_massive_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/127795943/Duality_invariance_in_massive_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="24917390" 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/24917390/Some_aspects_of_the_quantization_ofp_forms_and_reducible_gauge_theories">Some aspects of the quantization ofp-forms and reducible 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="47899957" href="https://unina.academia.edu/GaetanoFiore">Gaetano Fiore</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Il Nuovo Cimento A, 1991</p><p class="ds-related-work--abstract ds2-5-body-sm">The quantization of the p-form in D dimensions is carried out according to both an extension of the BRST formalism and a method due to A. S. Schwarz. The latter yields a suggestive interpretation of the role of nonphysical fields in the quantization of reducible gauge theories. The introduction of gauge conditions of a different type (namely self-dual) modifies the ghost spectrum but does not affect the partition function. PACS 11.15. -Gauge field theories. PACS 03.70. -Theories of quantized fields. 1. -Many examples of reducible gauge theories such as supergravity and string theories have arisen in the past decade. The term ,,reducible~ is currently understood to mean that the generators of the local gauge algebra which naturally appear in the formulation of the theory are linearly dependent on each other. Using a fairly condensed notation, (r being the set of the fields, S(r the classical action, R~ and ~ the gauge generators and the gauge parameters, respectively, gauge invariance implies ~S R~ (1) ~ ~ = O. (*) The authors of this paper have agreed to not receive the proofs for correction. 56 -I1 Nuovo Cimento A 899 ~00 L. CAPPIELLO and G. FIORE</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":"Some aspects of the quantization ofp-forms and reducible gauge theories","attachmentId":45245787,"attachmentType":"pdf","work_url":"https://www.academia.edu/24917390/Some_aspects_of_the_quantization_ofp_forms_and_reducible_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/24917390/Some_aspects_of_the_quantization_ofp_forms_and_reducible_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="92362424" 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/92362424/Gauge_theories_duality_relations_and_the_tensor_hierarchy">Gauge theories, duality relations and the tensor hierarchy</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="48717732" href="https://independent.academia.edu/MechthildHuebscher">Mechthild Huebscher</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of High Energy Physics, 2009</p><p class="ds-related-work--abstract ds2-5-body-sm">We compute the complete 3-and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the pform fields in the action and those of the same fields in the tensor hierarchy.</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, duality relations and the tensor hierarchy","attachmentId":95391080,"attachmentType":"pdf","work_url":"https://www.academia.edu/92362424/Gauge_theories_duality_relations_and_the_tensor_hierarchy","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/92362424/Gauge_theories_duality_relations_and_the_tensor_hierarchy"><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":46568564,"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":46568564,"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_46568564" 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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href="https://www.academia.edu/47024057/Mass_generation_in_Abelian_U_1_gauge_theories_A_rich_network_of_dualities">Mass generation in Abelian U(1) gauge theories: A rich network of dualities</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="7844450" href="https://independent.academia.edu/JanGovaerts">Jan Govaerts</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Mathematical Physics</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":"Mass generation in Abelian U(1) gauge theories: A rich network of dualities","attachmentId":66340398,"attachmentType":"pdf","work_url":"https://www.academia.edu/47024057/Mass_generation_in_Abelian_U_1_gauge_theories_A_rich_network_of_dualities","alternativeTracking":true}"><span class="material-symbols-outlined" 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class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="26736855" href="https://independent.academia.edu/ABDUSSALAM71">ABDUS SALAM</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Journal of Modern Physics A, 2005</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":"Doublet Groups, Extended Lie Algebras, and Well Defined Gauge Theories for the Two-Form Field","attachmentId":47002862,"attachmentType":"pdf","work_url":"https://www.academia.edu/26722499/Doublet_Groups_Extended_Lie_Algebras_and_Well_Defined_Gauge_Theories_for_the_Two_Form_Field","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 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