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Verlinde","profile_url":"https://independent.academia.edu/ErikVerlinde?f_ri=403158","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=403158","nofollow":false},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=403158","nofollow":false},{"id":514,"name":"Nuclear Physics","url":"https://www.academia.edu/Documents/in/Nuclear_Physics?f_ri=403158","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false},{"id":2578,"name":"Particle Physics","url":"https://www.academia.edu/Documents/in/Particle_Physics?f_ri=403158"},{"id":108262,"name":"Gauge theory","url":"https://www.academia.edu/Documents/in/Gauge_theory?f_ri=403158"},{"id":154543,"name":"Space 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href="https://www.academia.edu/11181345/Twisted_N_2_coset_models_Discrete_torsion_and_asymmetric_heterotic_string_compactifications">Twisted N = 2 coset models: Discrete torsion and asymmetric heterotic string compactifications</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/11181345" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="a2ab70ef99e2ab0e4ac6610ad4cf1590" rel="nofollow" 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href="https://www.academia.edu/Documents/in/Quantum_Physics">Quantum Physics</a>, <script data-card-contents-for-ri="518" type="text/json">{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="17324" href="https://www.academia.edu/Documents/in/Tensor_product_semigroups">Tensor product semigroups</a>, <script data-card-contents-for-ri="17324" type="text/json">{"id":17324,"name":"Tensor product semigroups","url":"https://www.academia.edu/Documents/in/Tensor_product_semigroups?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="143505" href="https://www.academia.edu/Documents/in/Calabi-Yau">Calabi-Yau</a><script data-card-contents-for-ri="143505" 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Quevedo","profile_url":"https://independent.academia.edu/FernandoMar%C3%ADnQuevedo?f_ri=403158","photo":"https://0.academia-photos.com/27001349/7583865/8513315/s65_fernando.mar_n_quevedo.jpg_oh_d49099338ec6ecb743a41eec269a8650_oe_557ff4da___gda___1435488748_7e903e09d9442ac5809a06c18fabe226"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=403158","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false},{"id":17324,"name":"Tensor product semigroups","url":"https://www.academia.edu/Documents/in/Tensor_product_semigroups?f_ri=403158","nofollow":false},{"id":143505,"name":"Calabi-Yau","url":"https://www.academia.edu/Documents/in/Calabi-Yau?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"},{"id":474077,"name":"Large classes","url":"https://www.academia.edu/Documents/in/Large_classes?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_60109488" data-work_id="60109488" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/60109488/Magnetofluid_Unification_in_Yang_Mills_Lagrangian">Magnetofluid Unification in Yang-Mills Lagrangian</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">The magnetofluid unification is constructed using lagrangian approach by imposing a non-Abelian gauge symmetry to the matter inside the fluid. The model provides a general description for relativistic fluid interacting with either Abelian... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_60109488" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The magnetofluid unification is constructed using lagrangian approach by imposing a non-Abelian gauge symmetry to the matter inside the fluid. The model provides a general description for relativistic fluid interacting with either Abelian or non-Abelian gauge field. The differences with the hybrid magnetofluid model are discussed, and some physical consequences of this formalism are briefly worked out.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/60109488" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="aa30270f9a2509087197cf4b75ab27ea" rel="nofollow" data-download="{"attachment_id":73695422,"asset_id":60109488,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/73695422/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="6686027" href="https://independent.academia.edu/albertussulaiman">albertus sulaiman</a><script data-card-contents-for-user="6686027" type="text/json">{"id":6686027,"first_name":"albertus","last_name":"sulaiman","domain_name":"independent","page_name":"albertussulaiman","display_name":"albertus sulaiman","profile_url":"https://independent.academia.edu/albertussulaiman?f_ri=403158","photo":"https://0.academia-photos.com/6686027/2919931/3414577/s65_albertus.sulaiman.jpg"}</script></span></span></li><li class="js-paper-rank-work_60109488 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="60109488"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 60109488, container: ".js-paper-rank-work_60109488", }); 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$(".js-view-count[data-work-id=60109488]").text(description); $(".js-view-count-work_60109488").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_60109488").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="60109488"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">3</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="403158" href="https://www.academia.edu/Documents/in/Gauge_Field">Gauge Field</a>, <script data-card-contents-for-ri="403158" type="text/json">{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1300799" href="https://www.academia.edu/Documents/in/Yang-Mills_Theory">Yang-Mills Theory</a>, <script data-card-contents-for-ri="1300799" type="text/json">{"id":1300799,"name":"Yang-Mills Theory","url":"https://www.academia.edu/Documents/in/Yang-Mills_Theory?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1411738" href="https://www.academia.edu/Documents/in/Gauge_Symmetry">Gauge Symmetry</a><script data-card-contents-for-ri="1411738" type="text/json">{"id":1411738,"name":"Gauge Symmetry","url":"https://www.academia.edu/Documents/in/Gauge_Symmetry?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=60109488]'), work: {"id":60109488,"title":"Magnetofluid Unification in Yang-Mills Lagrangian","created_at":"2021-10-26T22:39:40.041-07:00","url":"https://www.academia.edu/60109488/Magnetofluid_Unification_in_Yang_Mills_Lagrangian?f_ri=403158","dom_id":"work_60109488","summary":"The magnetofluid unification is constructed using lagrangian approach by imposing a non-Abelian gauge symmetry to the matter inside the fluid. The model provides a general description for relativistic fluid interacting with either Abelian or non-Abelian gauge field. The differences with the hybrid magnetofluid model are discussed, and some physical consequences of this formalism are briefly worked out.","downloadable_attachments":[{"id":73695422,"asset_id":60109488,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":6686027,"first_name":"albertus","last_name":"sulaiman","domain_name":"independent","page_name":"albertussulaiman","display_name":"albertus sulaiman","profile_url":"https://independent.academia.edu/albertussulaiman?f_ri=403158","photo":"https://0.academia-photos.com/6686027/2919931/3414577/s65_albertus.sulaiman.jpg"}],"research_interests":[{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false},{"id":1300799,"name":"Yang-Mills Theory","url":"https://www.academia.edu/Documents/in/Yang-Mills_Theory?f_ri=403158","nofollow":false},{"id":1411738,"name":"Gauge Symmetry","url":"https://www.academia.edu/Documents/in/Gauge_Symmetry?f_ri=403158","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_64294138" data-work_id="64294138" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/64294138/Noncommutative_Finsler_Geometry_Gauge_Fields_and_Gravity">Noncommutative Finsler Geometry, Gauge Fields and Gravity</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">AbstractThe work extends the A. Connes’ noncommutative geometry to spaces withgeneric local anisotropy. We apply the E. Cartan’s anholonomic frame approachto geometry models and physical theories and develop the nonlinear... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_64294138" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">AbstractThe work extends the A. Connes’ noncommutative geometry to spaces withgeneric local anisotropy. We apply the E. Cartan’s anholonomic frame approachto geometry models and physical theories and develop the nonlinear connectionformalism for projective modulespaces. Examples of noncommutative generationof anholonomic Riemann, Finsler and Lagrange spaces are analyzed. We alsopresent a research on noncommutative Finsler–gauge theories, generalized Finslergravity and anholonomic (pseudo) Riemann geometry which appear naturally ifanholonomic frames (vierbeins) are deﬁned in the context of string/M–theoryand extra dimension Riemann gravity..Pacs: 02.40.Gh, 02.40.-k, 04.50.+hMSC numbers: 83D05, 46L87, 58B34, 58B20, 53B40, 53C07 Contents 1 Introduction 22 Commutative and Noncommutative Spaces 42.1 Algebras of functions and (non) commutative spaces . . . . . . . . . . . 52.2 Commutative spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Noncommutative spaces . . . . . ....</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/64294138" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="917c646db569e5441ebc0a4c10ec873b" rel="nofollow" data-download="{"attachment_id":76394507,"asset_id":64294138,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/76394507/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="7910585" href="https://independent.academia.edu/VacaruSergiu">Sergiu Vacaru</a><script data-card-contents-for-user="7910585" type="text/json">{"id":7910585,"first_name":"Sergiu","last_name":"Vacaru","domain_name":"independent","page_name":"VacaruSergiu","display_name":"Sergiu Vacaru","profile_url":"https://independent.academia.edu/VacaruSergiu?f_ri=403158","photo":"https://0.academia-photos.com/7910585/2848048/18283457/s65_sergiu.vacaru.jpg"}</script></span></span></li><li class="js-paper-rank-work_64294138 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="64294138"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 64294138, container: ".js-paper-rank-work_64294138", }); 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$(".js-view-count[data-work-id=64294138]").text(description); $(".js-view-count-work_64294138").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_64294138").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="64294138"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">9</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="318" href="https://www.academia.edu/Documents/in/Mathematical_Physics">Mathematical Physics</a>, <script data-card-contents-for-ri="318" type="text/json">{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="6813" href="https://www.academia.edu/Documents/in/Quantum_Cosmology">Quantum Cosmology</a>, <script data-card-contents-for-ri="6813" type="text/json">{"id":6813,"name":"Quantum Cosmology","url":"https://www.academia.edu/Documents/in/Quantum_Cosmology?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="14024" href="https://www.academia.edu/Documents/in/High_Energy_Physics">High Energy Physics</a>, <script data-card-contents-for-ri="14024" type="text/json">{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="14348" href="https://www.academia.edu/Documents/in/Differential_Geometry">Differential Geometry</a><script data-card-contents-for-ri="14348" type="text/json">{"id":14348,"name":"Differential Geometry","url":"https://www.academia.edu/Documents/in/Differential_Geometry?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=64294138]'), work: {"id":64294138,"title":"Noncommutative Finsler Geometry, Gauge Fields and Gravity","created_at":"2021-12-15T06:30:57.225-08:00","url":"https://www.academia.edu/64294138/Noncommutative_Finsler_Geometry_Gauge_Fields_and_Gravity?f_ri=403158","dom_id":"work_64294138","summary":"AbstractThe work extends the A. Connes’ noncommutative geometry to spaces withgeneric local anisotropy. We apply the E. Cartan’s anholonomic frame approachto geometry models and physical theories and develop the nonlinear connectionformalism for projective modulespaces. Examples of noncommutative generationof anholonomic Riemann, Finsler and Lagrange spaces are analyzed. We alsopresent a research on noncommutative Finsler–gauge theories, generalized Finslergravity and anholonomic (pseudo) Riemann geometry which appear naturally ifanholonomic frames (vierbeins) are deﬁned in the context of string/M–theoryand extra dimension Riemann gravity..Pacs: 02.40.Gh, 02.40.-k, 04.50.+hMSC numbers: 83D05, 46L87, 58B34, 58B20, 53B40, 53C07 Contents 1 Introduction 22 Commutative and Noncommutative Spaces 42.1 Algebras of functions and (non) commutative spaces . . . . . . . . . . . 52.2 Commutative spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Noncommutative spaces . . . . . ....","downloadable_attachments":[{"id":76394507,"asset_id":64294138,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":7910585,"first_name":"Sergiu","last_name":"Vacaru","domain_name":"independent","page_name":"VacaruSergiu","display_name":"Sergiu Vacaru","profile_url":"https://independent.academia.edu/VacaruSergiu?f_ri=403158","photo":"https://0.academia-photos.com/7910585/2848048/18283457/s65_sergiu.vacaru.jpg"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=403158","nofollow":false},{"id":6813,"name":"Quantum Cosmology","url":"https://www.academia.edu/Documents/in/Quantum_Cosmology?f_ri=403158","nofollow":false},{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false},{"id":14348,"name":"Differential Geometry","url":"https://www.academia.edu/Documents/in/Differential_Geometry?f_ri=403158","nofollow":false},{"id":51108,"name":"Noncommutative Geometry","url":"https://www.academia.edu/Documents/in/Noncommutative_Geometry?f_ri=403158"},{"id":61108,"name":"Geometric model","url":"https://www.academia.edu/Documents/in/Geometric_model?f_ri=403158"},{"id":108262,"name":"Gauge theory","url":"https://www.academia.edu/Documents/in/Gauge_theory?f_ri=403158"},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"},{"id":2724088,"name":"M-projective module","url":"https://www.academia.edu/Documents/in/M-projective_module?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_20485342" data-work_id="20485342" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/20485342/Clifford_Finsler_algebroids_and_nonholonomic_Einstein_Dirac_structures">Clifford-Finsler algebroids and nonholonomic Einstein–Dirac structures</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/20485342" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="5f8b9e5fa194231f0a9a9fe85036910f" rel="nofollow" data-download="{"attachment_id":41398329,"asset_id":20485342,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/41398329/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa 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class="js-view-count-work_20485342 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="20485342"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 20485342; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=20485342]").text(description); $(".js-view-count-work_20485342").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_20485342").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="20485342"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">12</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="318" href="https://www.academia.edu/Documents/in/Mathematical_Physics">Mathematical Physics</a>, <script data-card-contents-for-ri="318" type="text/json">{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1247" href="https://www.academia.edu/Documents/in/Quantum_Gravity">Quantum Gravity</a>, <script data-card-contents-for-ri="1247" type="text/json">{"id":1247,"name":"Quantum Gravity","url":"https://www.academia.edu/Documents/in/Quantum_Gravity?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="14348" href="https://www.academia.edu/Documents/in/Differential_Geometry">Differential Geometry</a>, <script data-card-contents-for-ri="14348" type="text/json">{"id":14348,"name":"Differential Geometry","url":"https://www.academia.edu/Documents/in/Differential_Geometry?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="29972" href="https://www.academia.edu/Documents/in/Linear_Algebra">Linear Algebra</a><script data-card-contents-for-ri="29972" type="text/json">{"id":29972,"name":"Linear Algebra","url":"https://www.academia.edu/Documents/in/Linear_Algebra?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=20485342]'), work: {"id":20485342,"title":"Clifford-Finsler algebroids and nonholonomic Einstein–Dirac structures","created_at":"2016-01-22T00:46:48.148-08:00","url":"https://www.academia.edu/20485342/Clifford_Finsler_algebroids_and_nonholonomic_Einstein_Dirac_structures?f_ri=403158","dom_id":"work_20485342","summary":null,"downloadable_attachments":[{"id":41398329,"asset_id":20485342,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":7910585,"first_name":"Sergiu","last_name":"Vacaru","domain_name":"independent","page_name":"VacaruSergiu","display_name":"Sergiu Vacaru","profile_url":"https://independent.academia.edu/VacaruSergiu?f_ri=403158","photo":"https://0.academia-photos.com/7910585/2848048/18283457/s65_sergiu.vacaru.jpg"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=403158","nofollow":false},{"id":1247,"name":"Quantum Gravity","url":"https://www.academia.edu/Documents/in/Quantum_Gravity?f_ri=403158","nofollow":false},{"id":14348,"name":"Differential Geometry","url":"https://www.academia.edu/Documents/in/Differential_Geometry?f_ri=403158","nofollow":false},{"id":29972,"name":"Linear Algebra","url":"https://www.academia.edu/Documents/in/Linear_Algebra?f_ri=403158","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=403158"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences?f_ri=403158"},{"id":143488,"name":"Dirac equation","url":"https://www.academia.edu/Documents/in/Dirac_equation?f_ri=403158"},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"},{"id":403183,"name":"Dirac operator","url":"https://www.academia.edu/Documents/in/Dirac_operator?f_ri=403158"},{"id":875506,"name":"Physical Model","url":"https://www.academia.edu/Documents/in/Physical_Model?f_ri=403158"},{"id":1868639,"name":"Exact solution methods","url":"https://www.academia.edu/Documents/in/Exact_solution_methods?f_ri=403158"},{"id":1926934,"name":"Gauge Field Theory","url":"https://www.academia.edu/Documents/in/Gauge_Field_Theory?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_11113233" data-work_id="11113233" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/11113233/Exotic_R_4_and_quantum_field_theory">Exotic ℝ 4 and quantum field theory</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/11113233" 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correspond to the intermediate vector boson and the photon. These models may be renormalizable, and do not predict processes... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_64860689" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We construct unified models of weak and electromagnetic interactions using just three gauge fields which correspond to the intermediate vector boson and the photon. These models may be renormalizable, and do not predict processes involving neutral lepton currents.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/64860689" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="58a1833861539144f938c71dd61b3efc" rel="nofollow" data-download="{"attachment_id":76698538,"asset_id":64860689,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/76698538/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="63024496" href="https://independent.academia.edu/SheldonGlashow">Sheldon Glashow</a><script data-card-contents-for-user="63024496" type="text/json">{"id":63024496,"first_name":"Sheldon","last_name":"Glashow","domain_name":"independent","page_name":"SheldonGlashow","display_name":"Sheldon Glashow","profile_url":"https://independent.academia.edu/SheldonGlashow?f_ri=403158","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_64860689 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="64860689"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 64860689, container: ".js-paper-rank-work_64860689", }); 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These models may be renormalizable, and do not predict processes involving neutral lepton currents.","downloadable_attachments":[{"id":76698538,"asset_id":64860689,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":63024496,"first_name":"Sheldon","last_name":"Glashow","domain_name":"independent","page_name":"SheldonGlashow","display_name":"Sheldon Glashow","profile_url":"https://independent.academia.edu/SheldonGlashow?f_ri=403158","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=403158","nofollow":false},{"id":45100,"name":"Weak interaction","url":"https://www.academia.edu/Documents/in/Weak_interaction?f_ri=403158","nofollow":false},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false},{"id":459492,"name":"Unified Model","url":"https://www.academia.edu/Documents/in/Unified_Model?f_ri=403158"},{"id":1499498,"name":"High energy","url":"https://www.academia.edu/Documents/in/High_energy?f_ri=403158"},{"id":1760204,"name":"Elementary Particles","url":"https://www.academia.edu/Documents/in/Elementary_Particles?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_70175807" data-work_id="70175807" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/70175807/An_introduction_to_quantum_field_theory">An introduction to quantum field theory</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/70175807" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="0fb45dbf50b4cb8b218e054ee55b641c" rel="nofollow" data-download="{"attachment_id":80024335,"asset_id":70175807,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/80024335/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="57630554" href="https://independent.academia.edu/EVerlinde">Erik Verlinde</a><script data-card-contents-for-user="57630554" type="text/json">{"id":57630554,"first_name":"Erik","last_name":"Verlinde","domain_name":"independent","page_name":"EVerlinde","display_name":"Erik Verlinde","profile_url":"https://independent.academia.edu/EVerlinde?f_ri=403158","photo":"https://0.academia-photos.com/57630554/26499853/25048082/s65_erik.verlinde.jpg"}</script></span></span></li><li class="js-paper-rank-work_70175807 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="70175807"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 70175807, container: ".js-paper-rank-work_70175807", }); 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I begin by discussing global symmetries and show that they can be realized differently in nature, depending on whether or not the vacuum state is left invariant by... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_27617730" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In these lectures, I discuss the role of symmetries in particle physics. I begin by discussing global symmetries and show that they can be realized differently in nature, depending on whether or not the vacuum state is left invariant by the symmetry. I introduce next the notion of local symmetries and show how these symmetries can be implemented through the introduction of gauge fields. Using the simple example of a spontaneously broken U(1) symmetry, I discuss the Higgs mechanism showing that it provides a natural way for the gauge fields to acquire mass. Finally, I show how these concepts are used as the basis for the Standard Model of particle physics, ending with a brief description of some of the salient aspects of Quantum Chromodynamics and of the electroweak theory.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/27617730" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="6a7b8d82ed2c000a4b1e6948ac24d26d" rel="nofollow" data-download="{"attachment_id":47882596,"asset_id":27617730,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/47882596/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="51755056" href="https://independent.academia.edu/RobertoPeccei">Roberto Peccei</a><script data-card-contents-for-user="51755056" type="text/json">{"id":51755056,"first_name":"Roberto","last_name":"Peccei","domain_name":"independent","page_name":"RobertoPeccei","display_name":"Roberto Peccei","profile_url":"https://independent.academia.edu/RobertoPeccei?f_ri=403158","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_27617730 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="27617730"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 27617730, container: ".js-paper-rank-work_27617730", }); 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$(".js-view-count[data-work-id=27617730]").text(description); $(".js-view-count-work_27617730").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_27617730").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="27617730"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">5</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2578" href="https://www.academia.edu/Documents/in/Particle_Physics">Particle Physics</a>, <script data-card-contents-for-ri="2578" type="text/json">{"id":2578,"name":"Particle Physics","url":"https://www.academia.edu/Documents/in/Particle_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2712" href="https://www.academia.edu/Documents/in/Quantum_Chromodynamics">Quantum Chromodynamics</a>, <script data-card-contents-for-ri="2712" type="text/json">{"id":2712,"name":"Quantum Chromodynamics","url":"https://www.academia.edu/Documents/in/Quantum_Chromodynamics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="14024" href="https://www.academia.edu/Documents/in/High_Energy_Physics">High Energy Physics</a>, <script data-card-contents-for-ri="14024" type="text/json">{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="130616" href="https://www.academia.edu/Documents/in/Standard_Model">Standard Model</a><script data-card-contents-for-ri="130616" type="text/json">{"id":130616,"name":"Standard Model","url":"https://www.academia.edu/Documents/in/Standard_Model?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=27617730]'), work: {"id":27617730,"title":"Exact and Broken Symmetries in Particle Physics","created_at":"2016-08-08T03:57:40.046-07:00","url":"https://www.academia.edu/27617730/Exact_and_Broken_Symmetries_in_Particle_Physics?f_ri=403158","dom_id":"work_27617730","summary":"In these lectures, I discuss the role of symmetries in particle physics. I begin by discussing global symmetries and show that they can be realized differently in nature, depending on whether or not the vacuum state is left invariant by the symmetry. I introduce next the notion of local symmetries and show how these symmetries can be implemented through the introduction of gauge fields. Using the simple example of a spontaneously broken U(1) symmetry, I discuss the Higgs mechanism showing that it provides a natural way for the gauge fields to acquire mass. Finally, I show how these concepts are used as the basis for the Standard Model of particle physics, ending with a brief description of some of the salient aspects of Quantum Chromodynamics and of the electroweak theory.","downloadable_attachments":[{"id":47882596,"asset_id":27617730,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":51755056,"first_name":"Roberto","last_name":"Peccei","domain_name":"independent","page_name":"RobertoPeccei","display_name":"Roberto Peccei","profile_url":"https://independent.academia.edu/RobertoPeccei?f_ri=403158","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2578,"name":"Particle Physics","url":"https://www.academia.edu/Documents/in/Particle_Physics?f_ri=403158","nofollow":false},{"id":2712,"name":"Quantum Chromodynamics","url":"https://www.academia.edu/Documents/in/Quantum_Chromodynamics?f_ri=403158","nofollow":false},{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false},{"id":130616,"name":"Standard Model","url":"https://www.academia.edu/Documents/in/Standard_Model?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_27817030" data-work_id="27817030" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/27817030/Lectures_on_Open_Strings_and_Noncommutative_Gauge_Theories">Lectures on Open Strings, and Noncommutative Gauge Theories</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">In this notes the background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_27817030" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In this notes the background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these backgrounds are analyzed, and the generalizations to the orbifolded spaces are looked upon.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm 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class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="52136582" href="https://independent.academia.edu/NikitaNekrasov">Nikita Nekrasov</a><script data-card-contents-for-user="52136582" type="text/json">{"id":52136582,"first_name":"Nikita","last_name":"Nekrasov","domain_name":"independent","page_name":"NikitaNekrasov","display_name":"Nikita Nekrasov","profile_url":"https://independent.academia.edu/NikitaNekrasov?f_ri=403158","photo":"https://0.academia-photos.com/52136582/75400856/63919870/s65_nikita.nekrasov.jpg"}</script></span></span></li><li class="js-paper-rank-work_27817030 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="27817030"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() 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type="text/json">{"id":108262,"name":"Gauge theory","url":"https://www.academia.edu/Documents/in/Gauge_theory?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="143488" href="https://www.academia.edu/Documents/in/Dirac_equation">Dirac equation</a>, <script data-card-contents-for-ri="143488" type="text/json">{"id":143488,"name":"Dirac equation","url":"https://www.academia.edu/Documents/in/Dirac_equation?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="154543" href="https://www.academia.edu/Documents/in/Space_Time">Space Time</a>, <script data-card-contents-for-ri="154543" type="text/json">{"id":154543,"name":"Space Time","url":"https://www.academia.edu/Documents/in/Space_Time?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="403158" href="https://www.academia.edu/Documents/in/Gauge_Field">Gauge Field</a><script data-card-contents-for-ri="403158" type="text/json">{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=27817030]'), work: {"id":27817030,"title":"Lectures on Open Strings, and Noncommutative Gauge Theories","created_at":"2016-08-16T12:57:32.004-07:00","url":"https://www.academia.edu/27817030/Lectures_on_Open_Strings_and_Noncommutative_Gauge_Theories?f_ri=403158","dom_id":"work_27817030","summary":"In this notes the background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these backgrounds are analyzed, and the generalizations to the orbifolded spaces are looked upon.","downloadable_attachments":[{"id":48099598,"asset_id":27817030,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":52136582,"first_name":"Nikita","last_name":"Nekrasov","domain_name":"independent","page_name":"NikitaNekrasov","display_name":"Nikita Nekrasov","profile_url":"https://independent.academia.edu/NikitaNekrasov?f_ri=403158","photo":"https://0.academia-photos.com/52136582/75400856/63919870/s65_nikita.nekrasov.jpg"}],"research_interests":[{"id":108262,"name":"Gauge theory","url":"https://www.academia.edu/Documents/in/Gauge_theory?f_ri=403158","nofollow":false},{"id":143488,"name":"Dirac equation","url":"https://www.academia.edu/Documents/in/Dirac_equation?f_ri=403158","nofollow":false},{"id":154543,"name":"Space Time","url":"https://www.academia.edu/Documents/in/Space_Time?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false},{"id":410412,"name":"Equation of Motion","url":"https://www.academia.edu/Documents/in/Equation_of_Motion?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_27520139" data-work_id="27520139" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/27520139/Superstrings_Gauge_Fields_and_Black_Holes">Superstrings, Gauge Fields and Black Holes</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" 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window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=27520139]").text(description); $(".js-view-count-work_27520139").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_27520139").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="27520139"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">2</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="235060" href="https://www.academia.edu/Documents/in/Black_Hole">Black Hole</a>, <script data-card-contents-for-ri="235060" type="text/json">{"id":235060,"name":"Black Hole","url":"https://www.academia.edu/Documents/in/Black_Hole?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="403158" href="https://www.academia.edu/Documents/in/Gauge_Field">Gauge Field</a><script data-card-contents-for-ri="403158" type="text/json">{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=27520139]'), work: {"id":27520139,"title":"Superstrings, Gauge Fields and Black Holes","created_at":"2016-08-03T22:44:55.940-07:00","url":"https://www.academia.edu/27520139/Superstrings_Gauge_Fields_and_Black_Holes?f_ri=403158","dom_id":"work_27520139","summary":null,"downloadable_attachments":[{"id":47775921,"asset_id":27520139,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":6605420,"first_name":"Leong Chuan","last_name":"Kwek","domain_name":"nus","page_name":"LeongChuanKwek","display_name":"Leong Chuan Kwek","profile_url":"https://nus.academia.edu/LeongChuanKwek?f_ri=403158","photo":"https://0.academia-photos.com/6605420/2710056/3155488/s65_leong_chuan.kwek.jpg"}],"research_interests":[{"id":235060,"name":"Black Hole","url":"https://www.academia.edu/Documents/in/Black_Hole?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_30921559" data-work_id="30921559" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/30921559/Fiber_Bundles_and_Quantum_Theory">Fiber Bundles and Quantum Theory</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/30921559" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="dae4ef52e5ccb9cd770f53f1fda339ff" rel="nofollow" data-download="{"attachment_id":51346398,"asset_id":30921559,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/51346398/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="58820257" href="https://independent.academia.edu/BernsteinHerbert">Herbert Bernstein</a><script data-card-contents-for-user="58820257" type="text/json">{"id":58820257,"first_name":"Herbert","last_name":"Bernstein","domain_name":"independent","page_name":"BernsteinHerbert","display_name":"Herbert 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container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_30921559 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="30921559"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 30921559; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=30921559]").text(description); $(".js-view-count-work_30921559").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_30921559").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="30921559"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">17</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="300" href="https://www.academia.edu/Documents/in/Mathematics">Mathematics</a>, <script data-card-contents-for-ri="300" type="text/json">{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="333" href="https://www.academia.edu/Documents/in/Field_Theory">Field Theory</a>, <script data-card-contents-for-ri="333" type="text/json">{"id":333,"name":"Field Theory","url":"https://www.academia.edu/Documents/in/Field_Theory?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="512" href="https://www.academia.edu/Documents/in/Mechanics">Mechanics</a>, <script data-card-contents-for-ri="512" type="text/json">{"id":512,"name":"Mechanics","url":"https://www.academia.edu/Documents/in/Mechanics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="6811" href="https://www.academia.edu/Documents/in/Quantum_Theory">Quantum Theory</a><script data-card-contents-for-ri="6811" type="text/json">{"id":6811,"name":"Quantum Theory","url":"https://www.academia.edu/Documents/in/Quantum_Theory?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=30921559]'), work: {"id":30921559,"title":"Fiber Bundles and Quantum 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Theory","url":"https://www.academia.edu/Documents/in/Quantum_Theory?f_ri=403158","nofollow":false},{"id":7936,"name":"Quantum Mechanics","url":"https://www.academia.edu/Documents/in/Quantum_Mechanics?f_ri=403158"},{"id":10092,"name":"Quantum Field Theory","url":"https://www.academia.edu/Documents/in/Quantum_Field_Theory?f_ri=403158"},{"id":15118,"name":"Topology","url":"https://www.academia.edu/Documents/in/Topology?f_ri=403158"},{"id":34754,"name":"Magnetic field","url":"https://www.academia.edu/Documents/in/Magnetic_field?f_ri=403158"},{"id":75647,"name":"Interactions","url":"https://www.academia.edu/Documents/in/Interactions?f_ri=403158"},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"},{"id":920313,"name":"Electron Beam","url":"https://www.academia.edu/Documents/in/Electron_Beam?f_ri=403158"},{"id":951215,"name":"Invariance Principle","url":"https://www.academia.edu/Documents/in/Invariance_Principle?f_ri=403158"},{"id":1409149,"name":"Scientific American","url":"https://www.academia.edu/Documents/in/Scientific_American?f_ri=403158"},{"id":1760204,"name":"Elementary Particles","url":"https://www.academia.edu/Documents/in/Elementary_Particles?f_ri=403158"},{"id":1812670,"name":"Fermions","url":"https://www.academia.edu/Documents/in/Fermions?f_ri=403158"},{"id":2369196,"name":"Nucleons","url":"https://www.academia.edu/Documents/in/Nucleons?f_ri=403158"},{"id":2536781,"name":"baryons","url":"https://www.academia.edu/Documents/in/baryons?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_6230728" data-work_id="6230728" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/6230728/Emergent_Gravity_from_Noncommutative_Spacetime">Emergent Gravity from Noncommutative Spacetime</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">We showed before that self-dual electromagnetism in noncommutative (NC) spacetime is equivalent to self-dual Einstein gravity. This result implies a striking picture about gravity: Gravity can emerge from electromagnetism in NC spacetime.... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_6230728" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We showed before that self-dual electromagnetism in noncommutative (NC) spacetime is equivalent to self-dual Einstein gravity. This result implies a striking picture about gravity: Gravity can emerge from electromagnetism in NC spacetime. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy spacetime. We elucidate in some detail why electromagnetism in NC spacetime should be a theory of gravity. In particular, we show that NC electromagnetism is realized through the Darboux theorem as a diffeomorphism symmetry G which is spontaneously broken to symplectomorphism H due to a background symplectic two-form $B_{\mu\nu}=(1/\theta)_{\mu\nu}$, giving rise to NC spacetime. This leads to a natural speculation that the emergent gravity from NC electromagnetism corresponds to a nonlinear realization G/H of the diffeomorphism group, more generally its NC deformation. We also find some evidences that the emergent gravity contains the structure of generalized complex geometry and NC gravity. To illuminate the emergent gravity, we illustrate how self-dual NC electromagnetism nicely fits with the twistor space describing curved self-dual spacetime. We also discuss derivative corrections of Seiberg-Witten map which give rise to higher order gravity.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/6230728" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="c55d86b612968c76b4acaaf8738de04f" rel="nofollow" data-download="{"attachment_id":33096278,"asset_id":6230728,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/33096278/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="9569311" href="https://kias.academia.edu/HyunSeokYang">Hyun Seok Yang</a><script data-card-contents-for-user="9569311" type="text/json">{"id":9569311,"first_name":"Hyun Seok","last_name":"Yang","domain_name":"kias","page_name":"HyunSeokYang","display_name":"Hyun Seok Yang","profile_url":"https://kias.academia.edu/HyunSeokYang?f_ri=403158","photo":"https://0.academia-photos.com/9569311/3283841/3864351/s65_hyun_seok.yang.jpg"}</script></span></span></li><li class="js-paper-rank-work_6230728 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="6230728"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 6230728, container: ".js-paper-rank-work_6230728", }); 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$(".js-view-count[data-work-id=6230728]").text(description); $(".js-view-count-work_6230728").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_6230728").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="6230728"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">2</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="49247" href="https://www.academia.edu/Documents/in/Higher_Order_Thinking">Higher Order Thinking</a>, <script data-card-contents-for-ri="49247" type="text/json">{"id":49247,"name":"Higher Order Thinking","url":"https://www.academia.edu/Documents/in/Higher_Order_Thinking?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="403158" href="https://www.academia.edu/Documents/in/Gauge_Field">Gauge Field</a><script data-card-contents-for-ri="403158" type="text/json">{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=6230728]'), work: {"id":6230728,"title":"Emergent Gravity from Noncommutative Spacetime","created_at":"2014-02-27T16:06:10.927-08:00","url":"https://www.academia.edu/6230728/Emergent_Gravity_from_Noncommutative_Spacetime?f_ri=403158","dom_id":"work_6230728","summary":"We showed before that self-dual electromagnetism in noncommutative (NC) spacetime is equivalent to self-dual Einstein gravity. This result implies a striking picture about gravity: Gravity can emerge from electromagnetism in NC spacetime. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy spacetime. We elucidate in some detail why electromagnetism in NC spacetime should be a theory of gravity. In particular, we show that NC electromagnetism is realized through the Darboux theorem as a diffeomorphism symmetry G which is spontaneously broken to symplectomorphism H due to a background symplectic two-form $B_{\\mu\\nu}=(1/\\theta)_{\\mu\\nu}$, giving rise to NC spacetime. This leads to a natural speculation that the emergent gravity from NC electromagnetism corresponds to a nonlinear realization G/H of the diffeomorphism group, more generally its NC deformation. We also find some evidences that the emergent gravity contains the structure of generalized complex geometry and NC gravity. To illuminate the emergent gravity, we illustrate how self-dual NC electromagnetism nicely fits with the twistor space describing curved self-dual spacetime. We also discuss derivative corrections of Seiberg-Witten map which give rise to higher order gravity.","downloadable_attachments":[{"id":33096278,"asset_id":6230728,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":9569311,"first_name":"Hyun Seok","last_name":"Yang","domain_name":"kias","page_name":"HyunSeokYang","display_name":"Hyun Seok Yang","profile_url":"https://kias.academia.edu/HyunSeokYang?f_ri=403158","photo":"https://0.academia-photos.com/9569311/3283841/3864351/s65_hyun_seok.yang.jpg"}],"research_interests":[{"id":49247,"name":"Higher Order Thinking","url":"https://www.academia.edu/Documents/in/Higher_Order_Thinking?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_15268733" data-work_id="15268733" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/15268733/Duality_rotations_in_nonlinear_electrodynamics_and_in_extended_supergravity">Duality rotations in nonlinear electrodynamics and in extended supergravity</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">We review the general theory of duality rotations which, in four dimensions, exchange electric with magnetic fields. Necessary and sufficient conditions in order for a theory to have duality symmetry are established. A nontrivial example... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_15268733" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We review the general theory of duality rotations which, in four dimensions, exchange electric with magnetic fields. Necessary and sufficient conditions in order for a theory to have duality symmetry are established. A nontrivial example is Born-Infeld theory with n abelian gauge fields and with Sp(2n,R) self-duality. We then review duality symmetry in supergravity theories. In the case of N=2 supergravity duality rotations are in general not a symmetry of the theory but a key ingredient in order to formulate the theory itself. This is due to the beautiful relation between the geometry of special Kaehler manifolds and duality rotations.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/15268733" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="6ded92309f10540b6e0e5ededf96c940" rel="nofollow" data-download="{"attachment_id":38608279,"asset_id":15268733,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/38608279/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="34346070" href="https://independent.academia.edu/SergioFerrara1">Sergio Ferrara</a><script data-card-contents-for-user="34346070" type="text/json">{"id":34346070,"first_name":"Sergio","last_name":"Ferrara","domain_name":"independent","page_name":"SergioFerrara1","display_name":"Sergio Ferrara","profile_url":"https://independent.academia.edu/SergioFerrara1?f_ri=403158","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_15268733 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="15268733"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 15268733, container: ".js-paper-rank-work_15268733", }); 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$(".js-view-count[data-work-id=15268733]").text(description); $(".js-view-count-work_15268733").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_15268733").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="15268733"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">3</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="2578" href="https://www.academia.edu/Documents/in/Particle_Physics">Particle Physics</a>, <script data-card-contents-for-ri="2578" type="text/json">{"id":2578,"name":"Particle Physics","url":"https://www.academia.edu/Documents/in/Particle_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="34754" href="https://www.academia.edu/Documents/in/Magnetic_field">Magnetic field</a>, <script data-card-contents-for-ri="34754" type="text/json">{"id":34754,"name":"Magnetic field","url":"https://www.academia.edu/Documents/in/Magnetic_field?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="403158" href="https://www.academia.edu/Documents/in/Gauge_Field">Gauge Field</a><script data-card-contents-for-ri="403158" type="text/json">{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=15268733]'), work: {"id":15268733,"title":"Duality rotations in nonlinear electrodynamics and in extended supergravity","created_at":"2015-08-29T09:38:17.545-07:00","url":"https://www.academia.edu/15268733/Duality_rotations_in_nonlinear_electrodynamics_and_in_extended_supergravity?f_ri=403158","dom_id":"work_15268733","summary":"We review the general theory of duality rotations which, in four dimensions, exchange electric with magnetic fields. Necessary and sufficient conditions in order for a theory to have duality symmetry are established. A nontrivial example is Born-Infeld theory with n abelian gauge fields and with Sp(2n,R) self-duality. We then review duality symmetry in supergravity theories. In the case of N=2 supergravity duality rotations are in general not a symmetry of the theory but a key ingredient in order to formulate the theory itself. This is due to the beautiful relation between the geometry of special Kaehler manifolds and duality rotations.","downloadable_attachments":[{"id":38608279,"asset_id":15268733,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":34346070,"first_name":"Sergio","last_name":"Ferrara","domain_name":"independent","page_name":"SergioFerrara1","display_name":"Sergio Ferrara","profile_url":"https://independent.academia.edu/SergioFerrara1?f_ri=403158","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":2578,"name":"Particle Physics","url":"https://www.academia.edu/Documents/in/Particle_Physics?f_ri=403158","nofollow":false},{"id":34754,"name":"Magnetic field","url":"https://www.academia.edu/Documents/in/Magnetic_field?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 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this notes the background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_28309174" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In this notes the background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these backgrounds are analyzed, and the generalizations to the orbifolded spaces are looked upon.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" 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Mišković","profile_url":"https://pucv.academia.edu/OliveraMi%C5%A1kovi%C4%87?f_ri=403158","photo":"/images/s65_no_pic.png"},{"id":33729668,"first_name":"Jose","last_name":"Edelstein","domain_name":"usc-es","page_name":"JoseEdelstein","display_name":"Jose Edelstein","profile_url":"https://usc-es.academia.edu/JoseEdelstein?f_ri=403158","photo":"https://0.academia-photos.com/33729668/167455582/157409148/s65_jose.edelstein.jpeg"}],"research_interests":[{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false},{"id":235060,"name":"Black Hole","url":"https://www.academia.edu/Documents/in/Black_Hole?f_ri=403158","nofollow":false},{"id":313728,"name":"Cosmological Constant","url":"https://www.academia.edu/Documents/in/Cosmological_Constant?f_ri=403158","nofollow":false},{"id":364279,"name":"Chern Simons 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href="https://www.academia.edu/18359959/Baryon_Spectra_and_AdS_CFT_Correspondence">Baryon Spectra and AdS/CFT Correspondence</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">We provide a detailed map between wrapped D3-branes in Anti-de Sitter (AdS) backgrounds and dibaryon operators in the corresponding conformal field theory (CFT). The effective five dimensional action governing the dynamics of AdS space... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_18359959" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We provide a detailed map between wrapped D3-branes in Anti-de Sitter (AdS) backgrounds and dibaryon operators in the corresponding conformal field theory (CFT). The effective five dimensional action governing the dynamics of AdS space contains a U(1)R gauge field that mediates interactions between objects possessing R-charge. We show that the U(1)R charge of these wrapped D3-branes as measured by the</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/18359959" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="c626b72b1fc9226bacf4a8a6b5cdc0c2" rel="nofollow" data-download="{"attachment_id":40012880,"asset_id":18359959,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/40012880/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="38348607" href="https://independent.academia.edu/DavidBerenstein">David Berenstein</a><script data-card-contents-for-user="38348607" type="text/json">{"id":38348607,"first_name":"David","last_name":"Berenstein","domain_name":"independent","page_name":"DavidBerenstein","display_name":"David Berenstein","profile_url":"https://independent.academia.edu/DavidBerenstein?f_ri=403158","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_18359959 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="18359959"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 18359959, container: ".js-paper-rank-work_18359959", }); 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We show that the U(1)R charge of these wrapped D3-branes as measured by the","downloadable_attachments":[{"id":40012880,"asset_id":18359959,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":38348607,"first_name":"David","last_name":"Berenstein","domain_name":"independent","page_name":"DavidBerenstein","display_name":"David Berenstein","profile_url":"https://independent.academia.edu/DavidBerenstein?f_ri=403158","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":333,"name":"Field Theory","url":"https://www.academia.edu/Documents/in/Field_Theory?f_ri=403158","nofollow":false},{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=403158","nofollow":false},{"id":98734,"name":"AdS/CFT 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type="text/json">{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2578" href="https://www.academia.edu/Documents/in/Particle_Physics">Particle Physics</a>, <script data-card-contents-for-ri="2578" type="text/json">{"id":2578,"name":"Particle Physics","url":"https://www.academia.edu/Documents/in/Particle_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="403158" href="https://www.academia.edu/Documents/in/Gauge_Field">Gauge Field</a><script data-card-contents-for-ri="403158" type="text/json">{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=27817001]'), work: {"id":27817001,"title":"Seiberg-Witten 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theory","url":"https://www.academia.edu/Documents/in/Gauge_theory?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="403158" href="https://www.academia.edu/Documents/in/Gauge_Field">Gauge Field</a><script data-card-contents-for-ri="403158" type="text/json">{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=24498077]'), work: {"id":24498077,"title":"Gauge theory of gravity and 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Curves","url":"https://www.academia.edu/Documents/in/Closed_Timelike_Curves?f_ri=403158","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=403158","nofollow":false},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences?f_ri=403158","nofollow":false},{"id":235060,"name":"Black Hole","url":"https://www.academia.edu/Documents/in/Black_Hole?f_ri=403158"},{"id":396664,"name":"De Sitter","url":"https://www.academia.edu/Documents/in/De_Sitter?f_ri=403158"},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"},{"id":1228946,"name":"Physical Properties","url":"https://www.academia.edu/Documents/in/Physical_Properties?f_ri=403158"},{"id":1636662,"name":"Coupling Constant","url":"https://www.academia.edu/Documents/in/Coupling_Constant?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div 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href="https://www.academia.edu/Documents/in/Dark_Energy">Dark Energy</a>, <script data-card-contents-for-ri="16620" type="text/json">{"id":16620,"name":"Dark Energy","url":"https://www.academia.edu/Documents/in/Dark_Energy?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="75000" href="https://www.academia.edu/Documents/in/Philosophy_and_Religious_Studies">Philosophy and Religious Studies</a>, <script data-card-contents-for-ri="75000" type="text/json">{"id":75000,"name":"Philosophy and Religious Studies","url":"https://www.academia.edu/Documents/in/Philosophy_and_Religious_Studies?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="80414" href="https://www.academia.edu/Documents/in/Mathematical_Sciences">Mathematical Sciences</a><script data-card-contents-for-ri="80414" type="text/json">{"id":80414,"name":"Mathematical 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Castro","profile_url":"https://utfsm.academia.edu/CarlosCastro?f_ri=403158","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":4102,"name":"Foundations of Physics","url":"https://www.academia.edu/Documents/in/Foundations_of_Physics?f_ri=403158","nofollow":false},{"id":16620,"name":"Dark Energy","url":"https://www.academia.edu/Documents/in/Dark_Energy?f_ri=403158","nofollow":false},{"id":75000,"name":"Philosophy and Religious Studies","url":"https://www.academia.edu/Documents/in/Philosophy_and_Religious_Studies?f_ri=403158","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=403158","nofollow":false},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences?f_ri=403158"},{"id":313728,"name":"Cosmological Constant","url":"https://www.academia.edu/Documents/in/Cosmological_Constant?f_ri=403158"},{"id":335361,"name":"Infrared","url":"https://www.academia.edu/Documents/in/Infrared?f_ri=403158"},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"},{"id":599863,"name":"Pioneer anomaly","url":"https://www.academia.edu/Documents/in/Pioneer_anomaly?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_30615601" data-work_id="30615601" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/30615601/Anti_symmetric_tensor_gauge_theories">Anti-symmetric tensor gauge theories</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/30615601" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="c022a99ed047b3a8ff89ac39ed3c4041" rel="nofollow" data-download="{"attachment_id":51064234,"asset_id":30615601,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/51064234/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" 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href="https://www.academia.edu/Documents/in/Mathematical_Physics">Mathematical Physics</a>, <script data-card-contents-for-ri="318" type="text/json">{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="518" href="https://www.academia.edu/Documents/in/Quantum_Physics">Quantum Physics</a>, <script data-card-contents-for-ri="518" type="text/json">{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="7936" href="https://www.academia.edu/Documents/in/Quantum_Mechanics">Quantum Mechanics</a>, <script data-card-contents-for-ri="7936" type="text/json">{"id":7936,"name":"Quantum Mechanics","url":"https://www.academia.edu/Documents/in/Quantum_Mechanics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="85563" href="https://www.academia.edu/Documents/in/Invariant_Theory">Invariant Theory</a><script data-card-contents-for-ri="85563" type="text/json">{"id":85563,"name":"Invariant Theory","url":"https://www.academia.edu/Documents/in/Invariant_Theory?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=30615601]'), work: {"id":30615601,"title":"Anti-symmetric tensor gauge theories","created_at":"2016-12-26T12:10:47.978-08:00","url":"https://www.academia.edu/30615601/Anti_symmetric_tensor_gauge_theories?f_ri=403158","dom_id":"work_30615601","summary":null,"downloadable_attachments":[{"id":51064234,"asset_id":30615601,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":52450179,"first_name":"Ted","last_name":"Clark","domain_name":"independent","page_name":"TedClark5","display_name":"Ted Clark","profile_url":"https://independent.academia.edu/TedClark5?f_ri=403158","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=403158","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false},{"id":7936,"name":"Quantum Mechanics","url":"https://www.academia.edu/Documents/in/Quantum_Mechanics?f_ri=403158","nofollow":false},{"id":85563,"name":"Invariant Theory","url":"https://www.academia.edu/Documents/in/Invariant_Theory?f_ri=403158","nofollow":false},{"id":108262,"name":"Gauge theory","url":"https://www.academia.edu/Documents/in/Gauge_theory?f_ri=403158"},{"id":347272,"name":"Second Order","url":"https://www.academia.edu/Documents/in/Second_Order?f_ri=403158"},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_73592417" data-work_id="73592417" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/73592417/Hiding_and_Confining_Charges_via">Hiding and Confining Charges via</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">We describe two interesting effects in wormhole physics. First, we find that a genuinely charged matter source may appear neutral to an external observer - a phenomenon opposite to the famous Misner-Wheeler &quot;charge without... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_73592417" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We describe two interesting effects in wormhole physics. First, we find that a genuinely charged matter source may appear neutral to an external observer - a phenomenon opposite to the famous Misner-Wheeler &quot;charge without charge&quot; effect. This phenomenon takes place when coupling a bulk gravity/nonlinear-gauge-field system to a charged lightlike brane as a matter source. The &quot;charge-hiding&quot; effect occurs in</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/73592417" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="cd6a8b09c0087ecd4e21b3f6951f17d1" rel="nofollow" data-download="{"attachment_id":82054484,"asset_id":73592417,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/82054484/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="54144808" href="https://independent.academia.edu/SvetlanaPacheva">Svetlana Pacheva</a><script data-card-contents-for-user="54144808" type="text/json">{"id":54144808,"first_name":"Svetlana","last_name":"Pacheva","domain_name":"independent","page_name":"SvetlanaPacheva","display_name":"Svetlana Pacheva","profile_url":"https://independent.academia.edu/SvetlanaPacheva?f_ri=403158","photo":"https://0.academia-photos.com/54144808/35786191/30901510/s65_svetlana.pacheva.jpg"}</script></span></span></li><li class="js-paper-rank-work_73592417 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="73592417"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 73592417, container: ".js-paper-rank-work_73592417", }); 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$(".js-view-count[data-work-id=73592417]").text(description); $(".js-view-count-work_73592417").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_73592417").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="73592417"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">5</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="6813" href="https://www.academia.edu/Documents/in/Quantum_Cosmology">Quantum Cosmology</a>, <script data-card-contents-for-ri="6813" type="text/json">{"id":6813,"name":"Quantum Cosmology","url":"https://www.academia.edu/Documents/in/Quantum_Cosmology?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="14024" href="https://www.academia.edu/Documents/in/High_Energy_Physics">High Energy Physics</a>, <script data-card-contents-for-ri="14024" type="text/json">{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="154543" href="https://www.academia.edu/Documents/in/Space_Time">Space Time</a>, <script data-card-contents-for-ri="154543" type="text/json">{"id":154543,"name":"Space Time","url":"https://www.academia.edu/Documents/in/Space_Time?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="235060" href="https://www.academia.edu/Documents/in/Black_Hole">Black Hole</a><script data-card-contents-for-ri="235060" type="text/json">{"id":235060,"name":"Black Hole","url":"https://www.academia.edu/Documents/in/Black_Hole?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=73592417]'), work: {"id":73592417,"title":"Hiding and Confining Charges via","created_at":"2022-03-12T03:24:04.142-08:00","url":"https://www.academia.edu/73592417/Hiding_and_Confining_Charges_via?f_ri=403158","dom_id":"work_73592417","summary":"We describe two interesting effects in wormhole physics. First, we find that a genuinely charged matter source may appear neutral to an external observer - a phenomenon opposite to the famous Misner-Wheeler \u0026quot;charge without charge\u0026quot; effect. This phenomenon takes place when coupling a bulk gravity/nonlinear-gauge-field system to a charged lightlike brane as a matter source. The \u0026quot;charge-hiding\u0026quot; effect occurs in","downloadable_attachments":[{"id":82054484,"asset_id":73592417,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":54144808,"first_name":"Svetlana","last_name":"Pacheva","domain_name":"independent","page_name":"SvetlanaPacheva","display_name":"Svetlana Pacheva","profile_url":"https://independent.academia.edu/SvetlanaPacheva?f_ri=403158","photo":"https://0.academia-photos.com/54144808/35786191/30901510/s65_svetlana.pacheva.jpg"}],"research_interests":[{"id":6813,"name":"Quantum Cosmology","url":"https://www.academia.edu/Documents/in/Quantum_Cosmology?f_ri=403158","nofollow":false},{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false},{"id":154543,"name":"Space Time","url":"https://www.academia.edu/Documents/in/Space_Time?f_ri=403158","nofollow":false},{"id":235060,"name":"Black Hole","url":"https://www.academia.edu/Documents/in/Black_Hole?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_2279828" data-work_id="2279828" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/2279828/Spontaneous_symmetry_breaking_in_a_classical_particle">Spontaneous symmetry breaking in a classical particle</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Due to the fact that only matter fields have phase, frequently is believed that the gauge principle can induce gauge fields only in quantum systems. But this is not necessary. This paper, of pedagogical scope, presents a classical system... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_2279828" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Due to the fact that only matter fields have phase, frequently is believed that the gauge principle can induce gauge fields only in quantum systems. But this is not necessary. This paper, of pedagogical scope, presents a classical system constituted by a particle in a classical potential, which is used as a model to illustrate the gauge principle and the spontaneous symmetry breaking. Those concepts appear in the study of second order phase transitions. Ferroelectricity, ferromagnetism, superconductivity, plasmons in a free electron gas, and the mass of vector bosons in the gauge field Yang-Mills theories, are some of the phenomena in which these transitions occur.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/2279828" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="38f5effc52a61322ad249c674111bdf3" rel="nofollow" data-download="{"attachment_id":50688005,"asset_id":2279828,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/50688005/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="2369274" href="https://udea.academia.edu/jorgemahecha">jorge mahecha</a><script data-card-contents-for-user="2369274" type="text/json">{"id":2369274,"first_name":"jorge","last_name":"mahecha","domain_name":"udea","page_name":"jorgemahecha","display_name":"jorge mahecha","profile_url":"https://udea.academia.edu/jorgemahecha?f_ri=403158","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_2279828 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="2279828"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 2279828, container: ".js-paper-rank-work_2279828", }); 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$(".js-view-count[data-work-id=2279828]").text(description); $(".js-view-count-work_2279828").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_2279828").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="2279828"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="14024" href="https://www.academia.edu/Documents/in/High_Energy_Physics">High Energy Physics</a>, <script data-card-contents-for-ri="14024" type="text/json">{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="80414" href="https://www.academia.edu/Documents/in/Mathematical_Sciences">Mathematical Sciences</a>, <script data-card-contents-for-ri="80414" type="text/json">{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="118582" href="https://www.academia.edu/Documents/in/Physical_sciences">Physical sciences</a>, <script data-card-contents-for-ri="118582" type="text/json">{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="173963" href="https://www.academia.edu/Documents/in/Phase_transition">Phase transition</a><script data-card-contents-for-ri="173963" type="text/json">{"id":173963,"name":"Phase transition","url":"https://www.academia.edu/Documents/in/Phase_transition?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=2279828]'), work: {"id":2279828,"title":"Spontaneous symmetry breaking in a classical particle","created_at":"2012-12-11T19:30:09.643-08:00","url":"https://www.academia.edu/2279828/Spontaneous_symmetry_breaking_in_a_classical_particle?f_ri=403158","dom_id":"work_2279828","summary":"Due to the fact that only matter fields have phase, frequently is believed that the gauge principle can induce gauge fields only in quantum systems. But this is not necessary. This paper, of pedagogical scope, presents a classical system constituted by a particle in a classical potential, which is used as a model to illustrate the gauge principle and the spontaneous symmetry breaking. Those concepts appear in the study of second order phase transitions. Ferroelectricity, ferromagnetism, superconductivity, plasmons in a free electron gas, and the mass of vector bosons in the gauge field Yang-Mills theories, are some of the phenomena in which these transitions occur.","downloadable_attachments":[{"id":50688005,"asset_id":2279828,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":2369274,"first_name":"jorge","last_name":"mahecha","domain_name":"udea","page_name":"jorgemahecha","display_name":"jorge mahecha","profile_url":"https://udea.academia.edu/jorgemahecha?f_ri=403158","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false},{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=403158","nofollow":false},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences?f_ri=403158","nofollow":false},{"id":173963,"name":"Phase transition","url":"https://www.academia.edu/Documents/in/Phase_transition?f_ri=403158","nofollow":false},{"id":347272,"name":"Second Order","url":"https://www.academia.edu/Documents/in/Second_Order?f_ri=403158"},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"},{"id":1295692,"name":"Yang Mills Theory","url":"https://www.academia.edu/Documents/in/Yang_Mills_Theory?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_22116432" data-work_id="22116432" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/22116432/Three_Dimensional_Quantum_Gravity_Coupled_to_Gauge_Fields">Three-Dimensional Quantum Gravity Coupled to Gauge Fields</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/22116432" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="63a19245e0078fcca958885cbf3a059c" rel="nofollow" data-download="{"attachment_id":42784083,"asset_id":22116432,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen 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class="u-positionAbsolute" data-has-card-for-ri-list="22116432"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">7</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="318" href="https://www.academia.edu/Documents/in/Mathematical_Physics">Mathematical Physics</a>, <script data-card-contents-for-ri="318" type="text/json">{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="518" href="https://www.academia.edu/Documents/in/Quantum_Physics">Quantum Physics</a>, <script data-card-contents-for-ri="518" type="text/json">{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1247" href="https://www.academia.edu/Documents/in/Quantum_Gravity">Quantum Gravity</a>, <script data-card-contents-for-ri="1247" type="text/json">{"id":1247,"name":"Quantum Gravity","url":"https://www.academia.edu/Documents/in/Quantum_Gravity?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="60658" href="https://www.academia.edu/Documents/in/Numerical_Simulation">Numerical Simulation</a><script data-card-contents-for-ri="60658" type="text/json">{"id":60658,"name":"Numerical Simulation","url":"https://www.academia.edu/Documents/in/Numerical_Simulation?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=22116432]'), work: {"id":22116432,"title":"Three-Dimensional Quantum Gravity Coupled to Gauge 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href="https://www.academia.edu/21140101/Physical_aspects_of_the_field_theoretical_description_of_two_dimensional_ideal_fluids">Physical aspects of the field-theoretical description of two-dimensional ideal fluids</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/21140101" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="622fee6e8a05180b180b42efd6e8057e" rel="nofollow" data-download="{"attachment_id":41732885,"asset_id":21140101,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" 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fluids","created_at":"2016-01-29T07:04:12.953-08:00","url":"https://www.academia.edu/21140101/Physical_aspects_of_the_field_theoretical_description_of_two_dimensional_ideal_fluids?f_ri=403158","dom_id":"work_21140101","summary":null,"downloadable_attachments":[{"id":41732885,"asset_id":21140101,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":9074413,"first_name":"Florin","last_name":"Spineanu","domain_name":"inflpr","page_name":"FlorinSpineanu","display_name":"Florin Spineanu","profile_url":"https://inflpr.academia.edu/FlorinSpineanu?f_ri=403158","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":333,"name":"Field Theory","url":"https://www.academia.edu/Documents/in/Field_Theory?f_ri=403158","nofollow":false},{"id":16496,"name":"Fluid Dynamics","url":"https://www.academia.edu/Documents/in/Fluid_Dynamics?f_ri=403158","nofollow":false},{"id":148995,"name":"Long 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Shinkai","profile_url":"https://independent.academia.edu/HShinkai?f_ri=403158","photo":"https://0.academia-photos.com/122116196/106138109/95344925/s65_hisaaki.shinkai.png"}],"research_interests":[{"id":333,"name":"Field Theory","url":"https://www.academia.edu/Documents/in/Field_Theory?f_ri=403158","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false},{"id":16619,"name":"Early Universe","url":"https://www.academia.edu/Documents/in/Early_Universe?f_ri=403158","nofollow":false},{"id":164885,"name":"Domain wall","url":"https://www.academia.edu/Documents/in/Domain_wall?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"},{"id":1134221,"name":"Cosmic String","url":"https://www.academia.edu/Documents/in/Cosmic_String?f_ri=403158"},{"id":1636662,"name":"Coupling Constant","url":"https://www.academia.edu/Documents/in/Coupling_Constant?f_ri=403158"},{"id":3735670,"name":"Critical value","url":"https://www.academia.edu/Documents/in/Critical_value?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_34825602" data-work_id="34825602" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/34825602/Non_commutative_Calculus_and_Discrete_Physics">Non-commutative Calculus and Discrete Physics</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Sequences of actions do not commute.. For example, the tick of a clock and the measurement of a position do not commute with one another, since the position will have moved to the next position after the tick. We adopt non-commutative... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_34825602" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Sequences of actions do not commute.. For example, the tick of a clock and the measurement of a position do not commute with one another, since the position will have moved to the next position after the tick. We adopt non-commutative calculus, with derivatives represented by commutators. In the beginning distinct derivatives do not commute with one another, providing curvature formalism so that the form of the curvature of a gauge field appears almost as soon as the calculus is defined. This provides context for the Feynman-Dyson derivation of electromagnetic formalism from commutators, and generalizations including the early appearance of the form of the Levi-Civita connection dervived from the Jacobi identity. In this version of non-commutative physics bare quantum mechanics (its commutation relations) appears as the flat background for all other constructions. Ascent to classical physics is obtained by replacing commutators with Poisson brackets that satisfy the Leibniz rule. An appendix on matrix algebra from a discrete point of view (Iterants) is provided. This paper will appear in the proceedings of the ANPA conference held in Cambridge, England in the summer of 2002.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/34825602" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="70410d7348e1b02ba40e0208a41df64f" rel="nofollow" data-download="{"attachment_id":54684064,"asset_id":34825602,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/54684064/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="1187729" href="https://uic.academia.edu/LouisHKauffman">Louis H Kauffman</a><script data-card-contents-for-user="1187729" type="text/json">{"id":1187729,"first_name":"Louis","last_name":"H Kauffman","domain_name":"uic","page_name":"LouisHKauffman","display_name":"Louis H Kauffman","profile_url":"https://uic.academia.edu/LouisHKauffman?f_ri=403158","photo":"https://0.academia-photos.com/1187729/18034522/18038702/s65_louis.h_kauffman.jpg"}</script></span></span></li><li class="js-paper-rank-work_34825602 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="34825602"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 34825602, container: ".js-paper-rank-work_34825602", }); 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For example, the tick of a clock and the measurement of a position do not commute with one another, since the position will have moved to the next position after the tick. We adopt non-commutative calculus, with derivatives represented by commutators. In the beginning distinct derivatives do not commute with one another, providing curvature formalism so that the form of the curvature of a gauge field appears almost as soon as the calculus is defined. This provides context for the Feynman-Dyson derivation of electromagnetic formalism from commutators, and generalizations including the early appearance of the form of the Levi-Civita connection dervived from the Jacobi identity. In this version of non-commutative physics bare quantum mechanics (its commutation relations) appears as the flat background for all other constructions. Ascent to classical physics is obtained by replacing commutators with Poisson brackets that satisfy the Leibniz rule. An appendix on matrix algebra from a discrete point of view (Iterants) is provided. This paper will appear in the proceedings of the ANPA conference held in Cambridge, England in the summer of 2002.","downloadable_attachments":[{"id":54684064,"asset_id":34825602,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":1187729,"first_name":"Louis","last_name":"H Kauffman","domain_name":"uic","page_name":"LouisHKauffman","display_name":"Louis H Kauffman","profile_url":"https://uic.academia.edu/LouisHKauffman?f_ri=403158","photo":"https://0.academia-photos.com/1187729/18034522/18038702/s65_louis.h_kauffman.jpg"}],"research_interests":[{"id":7936,"name":"Quantum Mechanics","url":"https://www.academia.edu/Documents/in/Quantum_Mechanics?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false},{"id":679783,"name":"Boolean Satisfiability","url":"https://www.academia.edu/Documents/in/Boolean_Satisfiability?f_ri=403158","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_27659372" data-work_id="27659372" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/27659372/Axions_from_intersecting_branes_and_decoupled_chiral_fermions_at_the_Large_Hadron_Collider">Axions from intersecting branes and decoupled chiral fermions at the Large Hadron Collider</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/27659372" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="35e5f4aaf8abc298c3c60342e428ca4e" rel="nofollow" data-download="{"attachment_id":47924980,"asset_id":27659372,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/47924980/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="48644585" href="https://manchester.academia.edu/MarcoGuzzi">Marco Guzzi</a><script data-card-contents-for-user="48644585" type="text/json">{"id":48644585,"first_name":"Marco","last_name":"Guzzi","domain_name":"manchester","page_name":"MarcoGuzzi","display_name":"Marco Guzzi","profile_url":"https://manchester.academia.edu/MarcoGuzzi?f_ri=403158","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_27659372 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="27659372"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 27659372, container: ".js-paper-rank-work_27659372", }); 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This edge transport is topologically protected and dissipationless. Until recently, all existing... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_11167532" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing topological insulators, known as quantum Hall states, violated time-reversal symmetry. However, the discovery of the quantum spin Hall effect demonstrated the existence of novel topological states not rooted in time-reversal violations. Here, we lay out an experiment to realize time-reversal topological insulators in ultra-cold atomic gases subjected to synthetic gauge fields in the near-field of an atom-chip. In particular, we introduce a feasible scheme to engineer sharp boundaries where the "edge states" are localized. Besides, this multi-band system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Due to their unprecedented controllability, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/11167532" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="40a642fed91d8c0ff719a2197889dd8f" rel="nofollow" data-download="{"attachment_id":36807947,"asset_id":11167532,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/36807947/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="26962777" href="https://independent.academia.edu/AlejandroBermudez2">Alejandro Bermudez</a><script data-card-contents-for-user="26962777" type="text/json">{"id":26962777,"first_name":"Alejandro","last_name":"Bermudez","domain_name":"independent","page_name":"AlejandroBermudez2","display_name":"Alejandro Bermudez","profile_url":"https://independent.academia.edu/AlejandroBermudez2?f_ri=403158","photo":"https://0.academia-photos.com/26962777/7560282/8488337/s65_alejandro.bermudez.jpg_oh_5bf20649f888d8bfb4238447341afb86_oe_558a4fdc___gda___1431047856_00a1f95fc90d5b4278acea91682d699c"}</script></span></span></li><li class="js-paper-rank-work_11167532 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="11167532"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 11167532, container: ".js-paper-rank-work_11167532", }); 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$(".js-view-count[data-work-id=11167532]").text(description); $(".js-view-count-work_11167532").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_11167532").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="11167532"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">11</a>  </div><span class="InlineList-item-text u-textTruncate u-pl10x"><a class="InlineList-item-text" data-has-card-for-ri="518" href="https://www.academia.edu/Documents/in/Quantum_Physics">Quantum Physics</a>, <script data-card-contents-for-ri="518" type="text/json">{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="118582" href="https://www.academia.edu/Documents/in/Physical_sciences">Physical sciences</a>, <script data-card-contents-for-ri="118582" type="text/json">{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="202566" href="https://www.academia.edu/Documents/in/Quantum_Computer">Quantum Computer</a>, <script data-card-contents-for-ri="202566" type="text/json">{"id":202566,"name":"Quantum Computer","url":"https://www.academia.edu/Documents/in/Quantum_Computer?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="216003" href="https://www.academia.edu/Documents/in/Cold_Atoms_Physics">Cold Atoms Physics</a><script data-card-contents-for-ri="216003" type="text/json">{"id":216003,"name":"Cold Atoms Physics","url":"https://www.academia.edu/Documents/in/Cold_Atoms_Physics?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=11167532]'), work: {"id":11167532,"title":"Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms","created_at":"2015-02-28T10:36:04.236-08:00","url":"https://www.academia.edu/11167532/Engineering_Time_Reversal_Invariant_Topological_Insulators_With_Ultra_Cold_Atoms?f_ri=403158","dom_id":"work_11167532","summary":"Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing topological insulators, known as quantum Hall states, violated time-reversal symmetry. However, the discovery of the quantum spin Hall effect demonstrated the existence of novel topological states not rooted in time-reversal violations. Here, we lay out an experiment to realize time-reversal topological insulators in ultra-cold atomic gases subjected to synthetic gauge fields in the near-field of an atom-chip. In particular, we introduce a feasible scheme to engineer sharp boundaries where the \"edge states\" are localized. Besides, this multi-band system has a large parameter space exhibiting a variety of quantum phase transitions between topological and normal insulating phases. Due to their unprecedented controllability, cold-atom systems are ideally suited to realize topological states of matter and drive the development of topological quantum computing.","downloadable_attachments":[{"id":36807947,"asset_id":11167532,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":26962777,"first_name":"Alejandro","last_name":"Bermudez","domain_name":"independent","page_name":"AlejandroBermudez2","display_name":"Alejandro Bermudez","profile_url":"https://independent.academia.edu/AlejandroBermudez2?f_ri=403158","photo":"https://0.academia-photos.com/26962777/7560282/8488337/s65_alejandro.bermudez.jpg_oh_5bf20649f888d8bfb4238447341afb86_oe_558a4fdc___gda___1431047856_00a1f95fc90d5b4278acea91682d699c"}],"research_interests":[{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=403158","nofollow":false},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences?f_ri=403158","nofollow":false},{"id":202566,"name":"Quantum Computer","url":"https://www.academia.edu/Documents/in/Quantum_Computer?f_ri=403158","nofollow":false},{"id":216003,"name":"Cold Atoms Physics","url":"https://www.academia.edu/Documents/in/Cold_Atoms_Physics?f_ri=403158","nofollow":false},{"id":235064,"name":"Time Reversal","url":"https://www.academia.edu/Documents/in/Time_Reversal?f_ri=403158"},{"id":322954,"name":"Chip","url":"https://www.academia.edu/Documents/in/Chip?f_ri=403158"},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158"},{"id":983074,"name":"Quantum Phase Transition","url":"https://www.academia.edu/Documents/in/Quantum_Phase_Transition?f_ri=403158"},{"id":1735044,"name":"Spin Orbit Coupling","url":"https://www.academia.edu/Documents/in/Spin_Orbit_Coupling?f_ri=403158"},{"id":1985814,"name":"Near Field","url":"https://www.academia.edu/Documents/in/Near_Field?f_ri=403158"},{"id":2236678,"name":"Quantum Spin Hall","url":"https://www.academia.edu/Documents/in/Quantum_Spin_Hall?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_18318064" data-work_id="18318064" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/18318064/Ramond_Ramond_flux_stabilization_of_D_branes">Ramond–Ramond flux stabilization of D-branes</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/18318064" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="1c99ad3aae2b1eec6dbc8932088e3df6" rel="nofollow" data-download="{"attachment_id":39991788,"asset_id":18318064,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/39991788/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="38213095" href="https://snu-kr.academia.edu/SoojongRey">Soo-jong Rey</a><script data-card-contents-for-user="38213095" type="text/json">{"id":38213095,"first_name":"Soo-jong","last_name":"Rey","domain_name":"snu-kr","page_name":"SoojongRey","display_name":"Soo-jong Rey","profile_url":"https://snu-kr.academia.edu/SoojongRey?f_ri=403158","photo":"https://0.academia-photos.com/38213095/10664255/11905231/s65_soo-jong.rey.jpg"}</script></span></span></li><li class="js-paper-rank-work_18318064 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="18318064"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 18318064, container: ".js-paper-rank-work_18318064", }); 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$(".js-view-count[data-work-id=18318064]").text(description); $(".js-view-count-work_18318064").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_18318064").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="18318064"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">4</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="81390" href="https://www.academia.edu/Documents/in/Interdisciplinary_research">Interdisciplinary research</a>, <script data-card-contents-for-ri="81390" type="text/json">{"id":81390,"name":"Interdisciplinary research","url":"https://www.academia.edu/Documents/in/Interdisciplinary_research?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="368515" href="https://www.academia.edu/Documents/in/Brane_World">Brane World</a>, <script data-card-contents-for-ri="368515" type="text/json">{"id":368515,"name":"Brane World","url":"https://www.academia.edu/Documents/in/Brane_World?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="403158" href="https://www.academia.edu/Documents/in/Gauge_Field">Gauge Field</a>, <script data-card-contents-for-ri="403158" type="text/json">{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="982035" href="https://www.academia.edu/Documents/in/International_Collaboration">International Collaboration</a><script data-card-contents-for-ri="982035" type="text/json">{"id":982035,"name":"International Collaboration","url":"https://www.academia.edu/Documents/in/International_Collaboration?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=18318064]'), work: {"id":18318064,"title":"Ramond–Ramond flux stabilization of D-branes","created_at":"2015-11-14T02:55:35.118-08:00","url":"https://www.academia.edu/18318064/Ramond_Ramond_flux_stabilization_of_D_branes?f_ri=403158","dom_id":"work_18318064","summary":null,"downloadable_attachments":[{"id":39991788,"asset_id":18318064,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":38213095,"first_name":"Soo-jong","last_name":"Rey","domain_name":"snu-kr","page_name":"SoojongRey","display_name":"Soo-jong Rey","profile_url":"https://snu-kr.academia.edu/SoojongRey?f_ri=403158","photo":"https://0.academia-photos.com/38213095/10664255/11905231/s65_soo-jong.rey.jpg"}],"research_interests":[{"id":81390,"name":"Interdisciplinary research","url":"https://www.academia.edu/Documents/in/Interdisciplinary_research?f_ri=403158","nofollow":false},{"id":368515,"name":"Brane World","url":"https://www.academia.edu/Documents/in/Brane_World?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false},{"id":982035,"name":"International Collaboration","url":"https://www.academia.edu/Documents/in/International_Collaboration?f_ri=403158","nofollow":false}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_18341520" data-work_id="18341520" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/18341520/Higher_Spin_Gauge_Fields_and_Duality">Higher-Spin Gauge Fields and Duality</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">We review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in $D$ dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_18341520" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in $D$ dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We also discuss duality transformations that give different field theory representations of the same physical degrees of freedom, and discuss the example of gravity in</div></div></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/18341520" data-share-source="work_strip" data-spinner="small_white_hide_contents"><i class="fa fa-plus"></i><span class="work-strip-link-text u-ml1x" data-content="button_text">Bookmark</span></a></div></li><li class="InlineList-item"><div class="download"><a id="c459e9d3303f4ba429cae3420673e607" rel="nofollow" data-download="{"attachment_id":40004140,"asset_id":18341520,"asset_type":"Work","always_allow_download":false,"track":null,"button_location":"work_strip","source":null,"hide_modal":null}" class="Button Button--sm Button--inverseGreen js-download-button prompt_button doc_download" href="https://www.academia.edu/attachments/40004140/download_file?st=MTczMjQyMjgyNyw4LjIyMi4yMDguMTQ2&s=work_strip"><i class="fa fa-arrow-circle-o-down fa-lg"></i><span class="u-textUppercase u-ml1x" data-content="button_text">Download</span></a></div></li><li class="InlineList-item"><ul class="InlineList InlineList--bordered u-ph0x"><li class="InlineList-item InlineList-item--bordered"><span class="InlineList-item-text">by <span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a class="u-tcGrayDark u-fw700" data-has-card-for-user="38331548" href="https://independent.academia.edu/DarioFrancia">Dario Francia</a><script data-card-contents-for-user="38331548" type="text/json">{"id":38331548,"first_name":"Dario","last_name":"Francia","domain_name":"independent","page_name":"DarioFrancia","display_name":"Dario Francia","profile_url":"https://independent.academia.edu/DarioFrancia?f_ri=403158","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_18341520 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="18341520"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 18341520, container: ".js-paper-rank-work_18341520", }); 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$(".js-view-count[data-work-id=18341520]").text(description); $(".js-view-count-work_18341520").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_18341520").removeClass('hidden') })</script></div></li><li class="InlineList-item u-positionRelative" style="max-width: 250px"><div class="u-positionAbsolute" data-has-card-for-ri-list="18341520"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">5</a>  </div><span class="InlineList-item-text u-textTruncate u-pl9x"><a class="InlineList-item-text" data-has-card-for-ri="333" href="https://www.academia.edu/Documents/in/Field_Theory">Field Theory</a>, <script data-card-contents-for-ri="333" type="text/json">{"id":333,"name":"Field Theory","url":"https://www.academia.edu/Documents/in/Field_Theory?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="14024" href="https://www.academia.edu/Documents/in/High_Energy_Physics">High Energy Physics</a>, <script data-card-contents-for-ri="14024" type="text/json">{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="108262" href="https://www.academia.edu/Documents/in/Gauge_theory">Gauge theory</a>, <script data-card-contents-for-ri="108262" type="text/json">{"id":108262,"name":"Gauge theory","url":"https://www.academia.edu/Documents/in/Gauge_theory?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="403158" href="https://www.academia.edu/Documents/in/Gauge_Field">Gauge Field</a><script data-card-contents-for-ri="403158" type="text/json">{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=18341520]'), work: {"id":18341520,"title":"Higher-Spin Gauge Fields and Duality","created_at":"2015-11-14T12:17:35.997-08:00","url":"https://www.academia.edu/18341520/Higher_Spin_Gauge_Fields_and_Duality?f_ri=403158","dom_id":"work_18341520","summary":"We review the construction of free gauge theories for gauge fields in arbitrary representations of the Lorentz group in $D$ dimensions. We describe the multi-form calculus which gives the natural geometric framework for these theories. We also discuss duality transformations that give different field theory representations of the same physical degrees of freedom, and discuss the example of gravity in","downloadable_attachments":[{"id":40004140,"asset_id":18341520,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":38331548,"first_name":"Dario","last_name":"Francia","domain_name":"independent","page_name":"DarioFrancia","display_name":"Dario Francia","profile_url":"https://independent.academia.edu/DarioFrancia?f_ri=403158","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":333,"name":"Field Theory","url":"https://www.academia.edu/Documents/in/Field_Theory?f_ri=403158","nofollow":false},{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=403158","nofollow":false},{"id":108262,"name":"Gauge theory","url":"https://www.academia.edu/Documents/in/Gauge_theory?f_ri=403158","nofollow":false},{"id":403158,"name":"Gauge Field","url":"https://www.academia.edu/Documents/in/Gauge_Field?f_ri=403158","nofollow":false},{"id":1242198,"name":"Degree of Freedom","url":"https://www.academia.edu/Documents/in/Degree_of_Freedom?f_ri=403158"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_67457334" data-work_id="67457334" itemscope="itemscope" itemtype="https://schema.org/ScholarlyArticle"><div class="header"><div class="title u-fontSerif u-fs22 u-lineHeight1_3"><a class="u-tcGrayDarkest js-work-link" href="https://www.academia.edu/67457334/Quantum_hair_and_quantum_gravity">Quantum hair and quantum gravity</a></div></div><div class="u-pb4x u-mt3x"></div><ul class="InlineList u-ph0x u-fs13"><li class="InlineList-item logged_in_only"><div class="share_on_academia_work_button"><a class="academia_share Button Button--inverseBlue Button--sm js-bookmark-button" data-academia-share="Work/67457334" 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type="text/json">{"id":80414,"name":"Mathematical Sciences","url":"https://www.academia.edu/Documents/in/Mathematical_Sciences?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="118582" href="https://www.academia.edu/Documents/in/Physical_sciences">Physical sciences</a>, <script data-card-contents-for-ri="118582" type="text/json">{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences?f_ri=403158","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="125513" href="https://www.academia.edu/Documents/in/Superconductors">Superconductors</a><script data-card-contents-for-ri="125513" type="text/json">{"id":125513,"name":"Superconductors","url":"https://www.academia.edu/Documents/in/Superconductors?f_ri=403158","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=52842821]'), work: 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