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overflow: hidden; text-overflow: ellipsis; -webkit-line-clamp: 3; -webkit-box-orient: vertical; }</style><div class="col-xs-12 clearfix"><div class="u-floatLeft"><h1 class="PageHeader-title u-m0x u-fs30">Mathematical Physics</h1><div class="u-tcGrayDark">120,223 Followers</div><div class="u-tcGrayDark u-mt2x">Recent papers in <b>Mathematical Physics</b></div></div></div></div></div></div><div class="TabbedNavigation"><div class="container"><div class="row"><div class="col-xs-12 clearfix"><ul class="nav u-m0x u-p0x list-inline u-displayFlex"><li class="active"><a href="https://www.academia.edu/Documents/in/Mathematical_Physics">Top Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematical_Physics/MostCited">Most Cited Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematical_Physics/MostDownloaded">Most Downloaded Papers</a></li><li><a href="https://www.academia.edu/Documents/in/Mathematical_Physics/MostRecent">Newest Papers</a></li><li><a class="" href="https://www.academia.edu/People/Mathematical_Physics">People</a></li></ul></div><style type="text/css">ul.nav{flex-direction:row}@media(max-width: 567px){ul.nav{flex-direction:column}.TabbedNavigation li{max-width:100%}.TabbedNavigation li.active{background-color:var(--background-grey, #dddde2)}.TabbedNavigation li.active:before,.TabbedNavigation li.active:after{display:none}}</style></div></div></div><div class="container"><div class="row"><div class="col-xs-12"><div class="u-displayFlex"><div class="u-flexGrow1"><div class="works"><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_34940695" data-work_id="34940695" 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/34940695/_Gravitational_Waves_a_Nobel_Prize_to_a_Non_Discovery_">" Gravitational Waves " : a Nobel Prize to a " Non-Discovery "</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">This study illustrates why it is physically impossible that LIGO's interferometers can really detect motions whose order of magnitude should be – as expected-10-19 meters (1/10,000 the size of a proton). And finally it shows why gravity –... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_34940695" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">This study illustrates why it is physically impossible that LIGO's interferometers can really detect motions whose order of magnitude should be – as expected-10-19 meters (1/10,000 the size of a proton). And finally it shows why gravity – as linked to the universal inertia according to the Mach's Principle-does not need any wave/energy to instantaneously synchronize.</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/34940695" 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="fa644c3bd8eaa39491ba0685fc45a501" rel="nofollow" data-download="{"attachment_id":54802698,"asset_id":34940695,"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/54802698/download_file?st=MTczMjQxNjQyNiw4LjIyMi4yMDguMTQ2&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="6704391" href="https://independent.academia.edu/AlbertoMiatello">Alberto Miatello</a><script data-card-contents-for-user="6704391" type="text/json">{"id":6704391,"first_name":"Alberto","last_name":"Miatello","domain_name":"independent","page_name":"AlbertoMiatello","display_name":"Alberto Miatello","profile_url":"https://independent.academia.edu/AlbertoMiatello?f_ri=318","photo":"https://0.academia-photos.com/6704391/2637050/3064740/s65_alberto.miatello.jpg"}</script></span></span></li><li class="js-paper-rank-work_34940695 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="34940695"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 34940695, container: ".js-paper-rank-work_34940695", }); 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And finally it shows why gravity – as linked to the universal inertia according to the Mach's Principle-does not need any wave/energy to instantaneously synchronize. ","downloadable_attachments":[{"id":54802698,"asset_id":34940695,"asset_type":"Work","always_allow_download":false},{"id":55168036,"asset_id":34940695,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":6704391,"first_name":"Alberto","last_name":"Miatello","domain_name":"independent","page_name":"AlbertoMiatello","display_name":"Alberto Miatello","profile_url":"https://independent.academia.edu/AlbertoMiatello?f_ri=318","photo":"https://0.academia-photos.com/6704391/2637050/3064740/s65_alberto.miatello.jpg"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=318","nofollow":false},{"id":888,"name":"Cosmology (Physics)","url":"https://www.academia.edu/Documents/in/Cosmology_Physics_?f_ri=318"},{"id":1246,"name":"Gravitation","url":"https://www.academia.edu/Documents/in/Gravitation?f_ri=318"},{"id":2578,"name":"Particle Physics","url":"https://www.academia.edu/Documents/in/Particle_Physics?f_ri=318"},{"id":49963,"name":"Gravity Equation","url":"https://www.academia.edu/Documents/in/Gravity_Equation?f_ri=318"},{"id":96054,"name":"Gravity Model","url":"https://www.academia.edu/Documents/in/Gravity_Model?f_ri=318"},{"id":459785,"name":"Mach's principle","url":"https://www.academia.edu/Documents/in/Machs_principle?f_ri=318"},{"id":823463,"name":"Modified theories of Gravity","url":"https://www.academia.edu/Documents/in/Modified_theories_of_Gravity?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_33870747" data-work_id="33870747" 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/33870747/Superfluid_Vacuum_Theory">Superfluid Vacuum Theory</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">The motive of this paper is to prove that space-time is a fluid, by showing that anything propagating in space-time medium, travels at light speed which follows the speed equation in a fluid given by, í µí±£ 2 =</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/33870747" 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="98587fadf2925f6b5978395dfa24d9e6" rel="nofollow" data-download="{"attachment_id":53848356,"asset_id":33870747,"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/53848356/download_file?st=MTczMjQxNjQyNiw4LjIyMi4yMDguMTQ2&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="26956363" href="https://independent.academia.edu/MihirJha6">Mihir Jha</a><script data-card-contents-for-user="26956363" type="text/json">{"id":26956363,"first_name":"Mihir","last_name":"Jha","domain_name":"independent","page_name":"MihirJha6","display_name":"Mihir Jha","profile_url":"https://independent.academia.edu/MihirJha6?f_ri=318","photo":"https://0.academia-photos.com/26956363/11651678/12992103/s65_mihir.jha.jpg_oh_1bc7748206f8b9584e19f894f0db0134_oe_57715ae0"}</script></span></span></li><li class="js-paper-rank-work_33870747 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="33870747"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 33870747, container: ".js-paper-rank-work_33870747", }); 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Eddington, 1938; Teller,... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_33227079" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In the last century, a small minority of physicists considered a hypothetical binary logarithmic connection between the large and the small constants of physics, which also implies a base-2 power law (Fürth, 1929; Eddington, 1938; Teller, 1948; Salam, 1970; Bastin, 1971; Sirag, 1980, 1983; Sanchez, Kotov and Bizouard, 2009, 2011, 2012; Kritov, 2013). This paper brings to attention a plausible triple electro-gravito-informational significance of the fine structure constant, with its implications in a plausible four fields unification pattern at Planck scales and the existence of life forms in our universe: this triple significance is based on the existence of a unifying global scaling factor of nature which appears in a hypothetical fine tuning of both big G magnitude and all the non-zero rest masses of the all the elementary particles in the Standard Model. Furthermore, this paper also proposes dimensional relativity hypothesis (DRH) stating that the 3D appearance of space (or the 4D nature of spacetime) may be actually explained by the relative magnitude of the photon quantum (angular) momentum (and the hypothetical graviton quantum momentum respectively) and this global scaling factor (GSF): DRH also includes a generalized electrograviton model (EGM) for any hypothetical graviton. This paper also proposes a set of strong (and very strong) gravity constants and a gravitational field varying with the energy (and length) scale, all with potential importance in the unification of the four fundamental fields. Each of these hypotheses is a potential update for the Standard Model of particle physics. <br /> <br />Keywords: fine structure constant with triple electro-gravito-informational significance; unifying global scaling factor of nature; four fields unification; the Standard Model of particle physics; dimensional relativity hypothesis; electrograviton model; life forms <br /> <br />#DONATIONS. Anyone can donate for dr. Dragoi’s independent research and original music at: <a href="https://www.paypal.com/donate/?hosted_button_id=AQYGGDVDR7KH2" rel="nofollow">https://www.paypal.com/donate/?hosted_button_id=AQYGGDVDR7KH2</a></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/33227079" 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="9a5d0df8dd81532b6423d2718b302941" rel="nofollow" data-download="{"attachment_id":53989689,"asset_id":33227079,"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/53989689/download_file?st=MTczMjQxNjQyNiw4LjIyMi4yMDguMTQ2&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="4733559" href="https://univermed-cdgm.academia.edu/AndreiLucianDragoi">Andrei Lucian Drăgoi (Dragoi)</a><script data-card-contents-for-user="4733559" type="text/json">{"id":4733559,"first_name":"Andrei Lucian","last_name":"Drăgoi (Dragoi)","domain_name":"univermed-cdgm","page_name":"AndreiLucianDragoi","display_name":"Andrei Lucian Drăgoi (Dragoi)","profile_url":"https://univermed-cdgm.academia.edu/AndreiLucianDragoi?f_ri=318","photo":"https://0.academia-photos.com/4733559/2003529/13622306/s65_andrei_lucian.dragoi.jpg"}</script></span></span></li><li class="js-paper-rank-work_33227079 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="33227079"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 33227079, container: ".js-paper-rank-work_33227079", }); 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$(".js-view-count[data-work-id=33227079]").text(description); $(".js-view-count-work_33227079").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_33227079").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="33227079"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">26</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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="498" href="https://www.academia.edu/Documents/in/Physics">Physics</a>, <script data-card-contents-for-ri="498" type="text/json">{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a>, <script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="504" href="https://www.academia.edu/Documents/in/Computational_Physics">Computational Physics</a><script data-card-contents-for-ri="504" type="text/json">{"id":504,"name":"Computational Physics","url":"https://www.academia.edu/Documents/in/Computational_Physics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=33227079]'), work: {"id":33227079,"title":"(FSC-TS preprint - version 6.0 - 25 pages - 17.07.2017) On a plausible triple electro-gravito-informational significance \nof the fine structure constant and its implications in a plausible four fields unification pattern at Planck scale and the existence of life forms in our universe","created_at":"2017-05-28T03:02:18.410-07:00","url":"https://www.academia.edu/33227079/_FSC_TS_preprint_version_6_0_25_pages_17_07_2017_On_a_plausible_triple_electro_gravito_informational_significance_of_the_fine_structure_constant_and_its_implications_in_a_plausible_four_fields_unification_pattern_at_Planck_scale_and_the_existence_of_life_forms_in_our_universe?f_ri=318","dom_id":"work_33227079","summary":"In the last century, a small minority of physicists considered a hypothetical binary logarithmic connection between the large and the small constants of physics, which also implies a base-2 power law (Fürth, 1929; Eddington, 1938; Teller, 1948; Salam, 1970; Bastin, 1971; Sirag, 1980, 1983; Sanchez, Kotov and Bizouard, 2009, 2011, 2012; Kritov, 2013). This paper brings to attention a plausible triple electro-gravito-informational significance of the fine structure constant, with its implications in a plausible four fields unification pattern at Planck scales and the existence of life forms in our universe: this triple significance is based on the existence of a unifying global scaling factor of nature which appears in a hypothetical fine tuning of both big G magnitude and all the non-zero rest masses of the all the elementary particles in the Standard Model. Furthermore, this paper also proposes dimensional relativity hypothesis (DRH) stating that the 3D appearance of space (or the 4D nature of spacetime) may be actually explained by the relative magnitude of the photon quantum (angular) momentum (and the hypothetical graviton quantum momentum respectively) and this global scaling factor (GSF): DRH also includes a generalized electrograviton model (EGM) for any hypothetical graviton. This paper also proposes a set of strong (and very strong) gravity constants and a gravitational field varying with the energy (and length) scale, all with potential importance in the unification of the four fundamental fields. Each of these hypotheses is a potential update for the Standard Model of particle physics.\r\n\r\nKeywords: fine structure constant with triple electro-gravito-informational significance; unifying global scaling factor of nature; four fields unification; the Standard Model of particle physics; dimensional relativity hypothesis; electrograviton model; life forms \r\n\r\n#DONATIONS. Anyone can donate for dr. Dragoi’s independent research and original music at: https://www.paypal.com/donate/?hosted_button_id=AQYGGDVDR7KH2","downloadable_attachments":[{"id":53989689,"asset_id":33227079,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":4733559,"first_name":"Andrei Lucian","last_name":"Drăgoi (Dragoi)","domain_name":"univermed-cdgm","page_name":"AndreiLucianDragoi","display_name":"Andrei Lucian Drăgoi (Dragoi)","profile_url":"https://univermed-cdgm.academia.edu/AndreiLucianDragoi?f_ri=318","photo":"https://0.academia-photos.com/4733559/2003529/13622306/s65_andrei_lucian.dragoi.jpg"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":504,"name":"Computational Physics","url":"https://www.academia.edu/Documents/in/Computational_Physics?f_ri=318","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=318"},{"id":888,"name":"Cosmology (Physics)","url":"https://www.academia.edu/Documents/in/Cosmology_Physics_?f_ri=318"},{"id":1246,"name":"Gravitation","url":"https://www.academia.edu/Documents/in/Gravitation?f_ri=318"},{"id":1247,"name":"Quantum Gravity","url":"https://www.academia.edu/Documents/in/Quantum_Gravity?f_ri=318"},{"id":2578,"name":"Particle Physics","url":"https://www.academia.edu/Documents/in/Particle_Physics?f_ri=318"},{"id":2640,"name":"Quantum Information","url":"https://www.academia.edu/Documents/in/Quantum_Information?f_ri=318"},{"id":3396,"name":"Foundations of Quantum Mechanics","url":"https://www.academia.edu/Documents/in/Foundations_of_Quantum_Mechanics?f_ri=318"},{"id":9138,"name":"Applied Physics","url":"https://www.academia.edu/Documents/in/Applied_Physics?f_ri=318"},{"id":10092,"name":"Quantum Field Theory","url":"https://www.academia.edu/Documents/in/Quantum_Field_Theory?f_ri=318"},{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=318"},{"id":17871,"name":"Physics Education","url":"https://www.academia.edu/Documents/in/Physics_Education?f_ri=318"},{"id":29125,"name":"Gravitational Waves","url":"https://www.academia.edu/Documents/in/Gravitational_Waves?f_ri=318"},{"id":49963,"name":"Gravity Equation","url":"https://www.academia.edu/Documents/in/Gravity_Equation?f_ri=318"},{"id":79394,"name":"Gravity","url":"https://www.academia.edu/Documents/in/Gravity?f_ri=318"},{"id":96054,"name":"Gravity Model","url":"https://www.academia.edu/Documents/in/Gravity_Model?f_ri=318"},{"id":317484,"name":"Fine Structure Constant","url":"https://www.academia.edu/Documents/in/Fine_Structure_Constant?f_ri=318"},{"id":553583,"name":"Graviton","url":"https://www.academia.edu/Documents/in/Graviton?f_ri=318"},{"id":1430346,"name":"Gravitons","url":"https://www.academia.edu/Documents/in/Gravitons?f_ri=318"},{"id":1569892,"name":"Graviton Propagator","url":"https://www.academia.edu/Documents/in/Graviton_Propagator?f_ri=318"},{"id":1636662,"name":"Coupling Constant","url":"https://www.academia.edu/Documents/in/Coupling_Constant?f_ri=318"},{"id":1921577,"name":"Gravitons \u0026 Gravitational Waves","url":"https://www.academia.edu/Documents/in/Gravitons_and_Gravitational_Waves?f_ri=318"},{"id":2215193,"name":"Graviton field","url":"https://www.academia.edu/Documents/in/Graviton_field?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_30504157" data-work_id="30504157" 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/30504157/_Method_Statistical_Analysis_And_Modification_Of_Gas_Equation">[Method] Statistical Analysis And Modification Of Gas Equation</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 paper, thermodynamical variables P, V, T have been taken under consideration of purely statistical implications on thermodynamics. Correlation has been established using Karl Pearson coefficient of correlation K_(P,V) and... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_30504157" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In this paper, thermodynamical variables P, V, T have been taken under consideration of purely statistical implications on thermodynamics. Correlation has been established using Karl Pearson coefficient of correlation K_(P,V) and cross-check has been subjected to Cauchy-Bunyakovsky-Schwarz inequality for negative correlation, series have been derived for even{R_((pressure,volume))^(even observations)} and odd number{R_((pressure,volume))^(odd observations)}of experimentally simulated data sets and have been consecutively  put on Spearman’s rank  Correlation Coefficient check. Further in paper, author explains the curve join post-critical temperature absolute minima on Van der Waal’s isothermal plot within macroscopic limit with r-th central moment〖 μ〗_r about (PV)i  frequency distributions by taking it in use to explain the kurtosis β_2 and skewness β_1, as how the curve join refutes the possibility of platykurtic distribution following Bernoulli inequality treatment. Regression between temperature and pressure, i.e. T_i=(_i^')t=a+bp_i  has been studied, and regression coefficient for isochor has been derived using least square method. Centuries old Gas equation has been subjected to statistical cross-checks, and hence finally in the paper, author concludes through statistical treatments, as it will also consider thermodynamical fluctuation in statistical ensemble, to project a more precise equation to relate gaseous thermodynamical variables preluding to a new approach towards understanding of thermodynamical systems in macrostate.</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/30504157" 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="cfd969d4fc4ad976e6b76ed24156104e" rel="nofollow" data-download="{"attachment_id":63949666,"asset_id":30504157,"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/63949666/download_file?st=MTczMjQxNjQyNiw4LjIyMi4yMDguMTQ2&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="50747305" href="https://independent.academia.edu/UjjawalKrishnam">Ujjawal Krishnam</a><script data-card-contents-for-user="50747305" type="text/json">{"id":50747305,"first_name":"Ujjawal","last_name":"Krishnam","domain_name":"independent","page_name":"UjjawalKrishnam","display_name":"Ujjawal Krishnam","profile_url":"https://independent.academia.edu/UjjawalKrishnam?f_ri=318","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_30504157 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="30504157"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 30504157, container: ".js-paper-rank-work_30504157", }); 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Correlation has been established using Karl Pearson coefficient of correlation K_(P,V) and cross-check has been subjected to Cauchy-Bunyakovsky-Schwarz inequality for negative correlation, series have been derived for even{R_((pressure,volume))^(even observations)} and odd number{R_((pressure,volume))^(odd observations)}of experimentally simulated data sets and have been consecutively put on Spearman’s rank Correlation Coefficient check. Further in paper, author explains the curve join post-critical temperature absolute minima on Van der Waal’s isothermal plot within macroscopic limit with r-th central moment〖 μ〗_r about (PV)i frequency distributions by taking it in use to explain the kurtosis β_2 and skewness β_1, as how the curve join refutes the possibility of platykurtic distribution following Bernoulli inequality treatment. Regression between temperature and pressure, i.e. T_i=(_i^')t=a+bp_i has been studied, and regression coefficient for isochor has been derived using least square method. Centuries old Gas equation has been subjected to statistical cross-checks, and hence finally in the paper, author concludes through statistical treatments, as it will also consider thermodynamical fluctuation in statistical ensemble, to project a more precise equation to relate gaseous thermodynamical variables preluding to a new approach towards understanding of thermodynamical systems in macrostate.","downloadable_attachments":[{"id":63949666,"asset_id":30504157,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":50747305,"first_name":"Ujjawal","last_name":"Krishnam","domain_name":"independent","page_name":"UjjawalKrishnam","display_name":"Ujjawal Krishnam","profile_url":"https://independent.academia.edu/UjjawalKrishnam?f_ri=318","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=318","nofollow":false},{"id":318,"name":"Mathematical 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Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="498" href="https://www.academia.edu/Documents/in/Physics">Physics</a>, <script data-card-contents-for-ri="498" type="text/json">{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a>, <script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="888" href="https://www.academia.edu/Documents/in/Cosmology_Physics_">Cosmology (Physics)</a><script data-card-contents-for-ri="888" type="text/json">{"id":888,"name":"Cosmology 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Theory","url":"https://www.academia.edu/Documents/in/The_Big_Bang_Theory?f_ri=318"},{"id":288755,"name":"Black Holes, Dark Energy, Dark Matter","url":"https://www.academia.edu/Documents/in/Black_Holes_Dark_Energy_Dark_Matter?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_46884055" data-work_id="46884055" 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/46884055/Effective_field_theory">Effective field theory</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">This are some note on effective field theory. The content are -Introduction -Classification of operator -Wilsonian action -Fermi Theory -Non relativistic QED -S matrix equivalence theorem -Loops and EFT -Low energy QED... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_46884055" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">This are some note on effective field theory. The content are <br /> <br />-Introduction <br />-Classification of operator <br />-Wilsonian action <br />-Fermi Theory  <br />-Non relativistic QED <br />-S matrix equivalence theorem <br /> <br />-Loops and EFT <br />-Low energy QED <br />-Birifrangence of vacuum <br />-Positivity bound <br />-Loops, dimension and EFT <br />-Accidental symmetries <br />-EFT at the non-perturbative level <br />-Anomalies in QFT <br />-Chiral anomaly in QED and pion decay <br /> <br />-Exercies</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/46884055" 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="1b0f869111beb98ca22649e583670b5c" rel="nofollow" data-download="{"attachment_id":67859250,"asset_id":46884055,"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/67859250/download_file?st=MTczMjQxNjQyNiw4LjIyMi4yMDguMTQ2&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="34076902" href="https://desy.academia.edu/AlessioMiscioscia">Alessio Miscioscia</a><script data-card-contents-for-user="34076902" type="text/json">{"id":34076902,"first_name":"Alessio","last_name":"Miscioscia","domain_name":"desy","page_name":"AlessioMiscioscia","display_name":"Alessio Miscioscia","profile_url":"https://desy.academia.edu/AlessioMiscioscia?f_ri=318","photo":"https://0.academia-photos.com/34076902/29617540/59814341/s65_alessio.miscioscia.jpeg"}</script></span></span></li><li class="js-paper-rank-work_46884055 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="46884055"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 46884055, container: ".js-paper-rank-work_46884055", }); 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$(".js-view-count[data-work-id=46884055]").text(description); $(".js-view-count-work_46884055").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_46884055").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="46884055"><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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a>, <script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="20074" href="https://www.academia.edu/Documents/in/Beyond_the_Standard_Model_Physics">Beyond the Standard Model Physics</a><script data-card-contents-for-ri="20074" type="text/json">{"id":20074,"name":"Beyond the Standard Model Physics","url":"https://www.academia.edu/Documents/in/Beyond_the_Standard_Model_Physics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=46884055]'), work: {"id":46884055,"title":"Effective field theory","created_at":"2021-04-15T04:58:48.117-07:00","url":"https://www.academia.edu/46884055/Effective_field_theory?f_ri=318","dom_id":"work_46884055","summary":"This are some note on effective field theory. The content are\r\n\r\n-Introduction\r\n-Classification of operator\r\n-Wilsonian action\r\n-Fermi Theory \r\n-Non relativistic QED\r\n-S matrix equivalence theorem\r\n\r\n-Loops and EFT\r\n-Low energy QED\r\n-Birifrangence of vacuum\r\n-Positivity bound\r\n-Loops, dimension and EFT\r\n-Accidental symmetries\r\n-EFT at the non-perturbative level\r\n-Anomalies in QFT\r\n-Chiral anomaly in QED and pion decay\r\n\r\n-Exercies \r\n\r\n","downloadable_attachments":[{"id":67859250,"asset_id":46884055,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":34076902,"first_name":"Alessio","last_name":"Miscioscia","domain_name":"desy","page_name":"AlessioMiscioscia","display_name":"Alessio Miscioscia","profile_url":"https://desy.academia.edu/AlessioMiscioscia?f_ri=318","photo":"https://0.academia-photos.com/34076902/29617540/59814341/s65_alessio.miscioscia.jpeg"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":2578,"name":"Particle Physics","url":"https://www.academia.edu/Documents/in/Particle_Physics?f_ri=318","nofollow":false},{"id":20074,"name":"Beyond the Standard Model Physics","url":"https://www.academia.edu/Documents/in/Beyond_the_Standard_Model_Physics?f_ri=318","nofollow":false},{"id":42836,"name":"Effective Field Theory","url":"https://www.academia.edu/Documents/in/Effective_Field_Theory?f_ri=318"},{"id":130616,"name":"Standard Model","url":"https://www.academia.edu/Documents/in/Standard_Model?f_ri=318"},{"id":1347565,"name":"Quntum Field Theory","url":"https://www.academia.edu/Documents/in/Quntum_Field_Theory?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_36694750" data-work_id="36694750" 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/36694750/NOTES_ON_FOURIER_TRANSFORMS">NOTES ON FOURIER TRANSFORMS</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest">xbrhxrthxrhtdthsxtsjwsj</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/36694750" 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="9f872bee22a85de2575cf321e945c987" rel="nofollow" data-download="{"attachment_id":56633673,"asset_id":36694750,"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/56633673/download_file?st=MTczMjQxNjQyNiw4LjIyMi4yMDguMTQ2&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="82026383" href="https://stanford.academia.edu/haddvrgzdgrgra">haddvrg zdgrgra</a><script data-card-contents-for-user="82026383" type="text/json">{"id":82026383,"first_name":"haddvrg","last_name":"zdgrgra","domain_name":"stanford","page_name":"haddvrgzdgrgra","display_name":"haddvrg zdgrgra","profile_url":"https://stanford.academia.edu/haddvrgzdgrgra?f_ri=318","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_36694750 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="36694750"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 36694750, container: ".js-paper-rank-work_36694750", }); 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These models describe the modes which live at the edge of a non-Abelian Chern-Simons theory with a boundary. Further, it... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_36603052" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">The importance of the WZW models stems in large part from their relationship to non-Abelian Chern-Simons theories. These models describe the modes which live at the edge of a non-Abelian Chern-Simons theory with a boundary. Further, it turns out that the braiding of their conformal blocks coincides with the braiding of the Wilson lines in the Chern-Simons theory. The WZW models are defined by the choice of gauge group G,which we will take to be SU (N), and a level k ∈ Z. These theories are denoted as SU (N) k. The CFT for a compact boson is a particularly simple example of a WZW model model with U (1) m. Unusual for the conformal field theories, the WZW models have a Lagrangian description where the action reads S = k 4π d 2 x Tr g −1 ∂ t gg −1 ∂ x g − v(g −1 ∂ x g) 2) + 2πkw(g). Here g ∈ G is a group valued field in d = 1 + 1 dimensions. The first term describes a chiral sigma model whose target space is the group manifold G. The second term is more subtle. It is defined as the integral over the full-three dimensional manifold M w(g) = 1 24π 2 M d 3 xx µνρ Tr(g −1 ∂ µ gg −1 ∂ ν gg −1 ∂ ρ g) which we recognize as the winding number. Taking the level k ∈ Z ensures that the two-dimensional theory on the boundary is actually independent of our choice of M. In this way, the WZW model is despite appearances an intrinsically a two-dimensional theory. The central charge of the SU (N) k WZW model is c = k(N 2 − 1) k + N. The theories are weakly coupled as k → ∞ where the central charge is equal to the dimension of the group SU (N). Theories become strongly coupled as k gets smaller. In particular, for k = 0 we have c = 0. This reflects the fact that the sigma-model on the group manifold without any topological term flows to a gapped theory in the infra-red. The WZW models have a large symmetry G known as a current algebra. Usually in quantum field theory, a symmetry implies a current J µ which obeys ∂ µ J µ = 0. The symmetry of the WZW model is much stronger as the left-moving and right-moving parts of the current are independently conserved. In terms of complex coordinates, this means that we have holomorphic and anti-holomorphic currents J = ∂gg −1 and J = g −1 ∂g obeying ∂J(z) = 0 and ∂J(z) = 0 respectively. This is very similar to the conditions on the energy-momentum tensor. The resulting modes obey [J a n , J b m ] = if ab c J c − n + m + knδ ab δ n+m. Here a, b label the different generators of the Lie algebra associated to G and f ab c are the structure constants of the Lie algebra. Meanwhile, n and m label the modes of the current algebra. Note that if we restrict our attention to the n, m = 0 sector then this contains the Lie algebra. Including all the modes gives an infinite dimensional generalization of the Lie algebra known as the Kac-Moody algebra. The representations of [J a n , J b m ] = if ab c J c − n + m + knδ ab δ n+m</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/36603052" 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="86eb433b4b0832bf9f11efdb57d69cf3" rel="nofollow" data-download="{"attachment_id":56531360,"asset_id":36603052,"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/56531360/download_file?st=MTczMjQxNjQyNiw4LjIyMi4yMDguMTQ2&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="2792810" href="https://independentresearcher.academia.edu/DrJMAshfaqueAMIMAMInstP">Dr. J. 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These models describe the modes which live at the edge of a non-Abelian Chern-Simons theory with a boundary. Further, it turns out that the braiding of their conformal blocks coincides with the braiding of the Wilson lines in the Chern-Simons theory. The WZW models are defined by the choice of gauge group G,which we will take to be SU (N), and a level k ∈ Z. These theories are denoted as SU (N) k. The CFT for a compact boson is a particularly simple example of a WZW model model with U (1) m. Unusual for the conformal field theories, the WZW models have a Lagrangian description where the action reads S = k 4π d 2 x Tr g −1 ∂ t gg −1 ∂ x g − v(g −1 ∂ x g) 2) + 2πkw(g). Here g ∈ G is a group valued field in d = 1 + 1 dimensions. The first term describes a chiral sigma model whose target space is the group manifold G. The second term is more subtle. It is defined as the integral over the full-three dimensional manifold M w(g) = 1 24π 2 M d 3 xx µνρ Tr(g −1 ∂ µ gg −1 ∂ ν gg −1 ∂ ρ g) which we recognize as the winding number. Taking the level k ∈ Z ensures that the two-dimensional theory on the boundary is actually independent of our choice of M. In this way, the WZW model is despite appearances an intrinsically a two-dimensional theory. The central charge of the SU (N) k WZW model is c = k(N 2 − 1) k + N. The theories are weakly coupled as k → ∞ where the central charge is equal to the dimension of the group SU (N). Theories become strongly coupled as k gets smaller. In particular, for k = 0 we have c = 0. This reflects the fact that the sigma-model on the group manifold without any topological term flows to a gapped theory in the infra-red. The WZW models have a large symmetry G known as a current algebra. Usually in quantum field theory, a symmetry implies a current J µ which obeys ∂ µ J µ = 0. The symmetry of the WZW model is much stronger as the left-moving and right-moving parts of the current are independently conserved. In terms of complex coordinates, this means that we have holomorphic and anti-holomorphic currents J = ∂gg −1 and J = g −1 ∂g obeying ∂J(z) = 0 and ∂J(z) = 0 respectively. This is very similar to the conditions on the energy-momentum tensor. The resulting modes obey [J a n , J b m ] = if ab c J c − n + m + knδ ab δ n+m. Here a, b label the different generators of the Lie algebra associated to G and f ab c are the structure constants of the Lie algebra. Meanwhile, n and m label the modes of the current algebra. Note that if we restrict our attention to the n, m = 0 sector then this contains the Lie algebra. Including all the modes gives an infinite dimensional generalization of the Lie algebra known as the Kac-Moody algebra. The representations of [J a n , J b m ] = if ab c J c − n + m + knδ ab δ n+m","downloadable_attachments":[{"id":56531360,"asset_id":36603052,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":2792810,"first_name":"Dr. J. M.","last_name":"Ashfaque (MInstP)","domain_name":"independentresearcher","page_name":"DrJMAshfaqueAMIMAMInstP","display_name":"Dr. J. M. Ashfaque (MInstP)","profile_url":"https://independentresearcher.academia.edu/DrJMAshfaqueAMIMAMInstP?f_ri=318","photo":"https://0.academia-photos.com/2792810/914293/18370870/s65_dr._j._m..ashfaque_amima_minstp_.jpg"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=318","nofollow":false},{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":10092,"name":"Quantum Field Theory","url":"https://www.academia.edu/Documents/in/Quantum_Field_Theory?f_ri=318"},{"id":14024,"name":"High Energy Physics","url":"https://www.academia.edu/Documents/in/High_Energy_Physics?f_ri=318"},{"id":154823,"name":"Conformal Field Theory","url":"https://www.academia.edu/Documents/in/Conformal_Field_Theory?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_36431548" data-work_id="36431548" 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/36431548/Circular_and_rectilinear_Sagnac_effects_are_dynamically_equivalent_and_contradictory_to_special_relativity_theory">Circular and rectilinear Sagnac effects are dynamically equivalent and contradictory to special relativity theory</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">To appear in Physics Essays, vol. 31, issue 2 (June, 2018) The Sagnac effect, named after its discoverer, is the phase shift occurring between two beams of light, traveling in opposite directions along a closed path around a moving... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_36431548" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">To appear in Physics Essays, vol. 31, issue 2 (June, 2018) <br /> <br />The Sagnac effect, named after its discoverer, is the phase shift occurring between two beams of light, traveling in opposite directions along a closed path around a moving object. A special case is the circular Sagnac effect, known for its crucial role in GPS and fiber-optic gyroscopes. It is often claimed that the circular Sagnac effect does not contradict special relativity theory (SRT) because it is considered an accelerated motion, while SRT applies only to uniform, non-accelerated motion. It is further claimed that the Sagnac effect, manifest in circular motion, should be treated in the framework of general relativity theory (GRT). We counter these arguments by underscoring the fact that the dynamics of rectilinear and circular types of motion are completely equivalent, and that this equivalence holds true for both non-accelerated and accelerated motion. With respect to the Sagnac effect, this equivalence means that a uniform circular motion (with constant w) is completely equivalent to a uniform rectilinear motion (with constant v). We support this conclusion by convincing experimental findings, indicating that an identical Sagnac effect to the one found in circular motion, exists in rectilinear uniform motion. We conclude that the circular Sagnac effect is fully explainable in the framework of inertial systems, and that the circular Sagnac effect contradicts special relativity theory and calls for its refutation. 2</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/36431548" 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="4027dc54f0cf8fe6e5794bf4bf2469b3" rel="nofollow" data-download="{"attachment_id":56460278,"asset_id":36431548,"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/56460278/download_file?st=MTczMjQxNjQyNiw4LjIyMi4yMDguMTQ2&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="24582379" href="https://haifa.academia.edu/RamziSuleiman">Ramzi Suleiman</a><script data-card-contents-for-user="24582379" type="text/json">{"id":24582379,"first_name":"Ramzi","last_name":"Suleiman","domain_name":"haifa","page_name":"RamziSuleiman","display_name":"Ramzi Suleiman","profile_url":"https://haifa.academia.edu/RamziSuleiman?f_ri=318","photo":"https://0.academia-photos.com/24582379/9731850/10840460/s65_ramzi.suleiman.jpg_oh_0c9a0b928958f21a43541e5d66c9c3a3_oe_562506c0___gda___1441770827_0261030fe69a17797a97ec91dffa3674"}</script></span></span></li><li class="js-paper-rank-work_36431548 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="36431548"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 36431548, container: ".js-paper-rank-work_36431548", }); 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$(".js-view-count[data-work-id=36431548]").text(description); $(".js-view-count-work_36431548").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_36431548").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="36431548"><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="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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a><script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=36431548]'), work: {"id":36431548,"title":"Circular and rectilinear Sagnac effects are dynamically equivalent and contradictory to special relativity theory","created_at":"2018-04-17T18:15:04.596-07:00","url":"https://www.academia.edu/36431548/Circular_and_rectilinear_Sagnac_effects_are_dynamically_equivalent_and_contradictory_to_special_relativity_theory?f_ri=318","dom_id":"work_36431548","summary":"To appear in Physics Essays, vol. 31, issue 2 (June, 2018)\r\n\r\nThe Sagnac effect, named after its discoverer, is the phase shift occurring between two beams of light, traveling in opposite directions along a closed path around a moving object. A special case is the circular Sagnac effect, known for its crucial role in GPS and fiber-optic gyroscopes. It is often claimed that the circular Sagnac effect does not contradict special relativity theory (SRT) because it is considered an accelerated motion, while SRT applies only to uniform, non-accelerated motion. It is further claimed that the Sagnac effect, manifest in circular motion, should be treated in the framework of general relativity theory (GRT). We counter these arguments by underscoring the fact that the dynamics of rectilinear and circular types of motion are completely equivalent, and that this equivalence holds true for both non-accelerated and accelerated motion. With respect to the Sagnac effect, this equivalence means that a uniform circular motion (with constant w) is completely equivalent to a uniform rectilinear motion (with constant v). We support this conclusion by convincing experimental findings, indicating that an identical Sagnac effect to the one found in circular motion, exists in rectilinear uniform motion. We conclude that the circular Sagnac effect is fully explainable in the framework of inertial systems, and that the circular Sagnac effect contradicts special relativity theory and calls for its refutation. 2","downloadable_attachments":[{"id":56460278,"asset_id":36431548,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":24582379,"first_name":"Ramzi","last_name":"Suleiman","domain_name":"haifa","page_name":"RamziSuleiman","display_name":"Ramzi Suleiman","profile_url":"https://haifa.academia.edu/RamziSuleiman?f_ri=318","photo":"https://0.academia-photos.com/24582379/9731850/10840460/s65_ramzi.suleiman.jpg_oh_0c9a0b928958f21a43541e5d66c9c3a3_oe_562506c0___gda___1441770827_0261030fe69a17797a97ec91dffa3674"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","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_36429904" data-work_id="36429904" 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/36429904/The_Hawking_Temperature_of_the_AdS_Schwarzschild_Black_Hole_from_Euclidean_Gravity">The Hawking Temperature of the AdS-Schwarzschild Black Hole from Euclidean 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">To compute the temperature of AdS black holes, we need to know the AdS metric. The Einstein equation for a (d + 2)-dimensional Minkowski-signature space-time with negative cosmological constant is R µν − 1 2 g µν R − d(d + 1) 2L 2 g µν =... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_36429904" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">To compute the temperature of AdS black holes, we need to know the AdS metric. The Einstein equation for a (d + 2)-dimensional Minkowski-signature space-time with negative cosmological constant is R µν − 1 2 g µν R − d(d + 1) 2L 2 g µν = 0. This is solved by an AdS-Schwarzschild black hole background with the metric ds 2 = r 2 L 2 (−f (r)dt 2 + dΣ 2 k) + L 2 r 2 f (r) dr 2 , i = 1, ..., d where L is the AdS radius and r is the radial direction while f (r) = 1 − m r d+1 +</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/36429904" 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="f9f84bb87066a580e41f2ebe5941dce1" rel="nofollow" data-download="{"attachment_id":56343277,"asset_id":36429904,"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/56343277/download_file?st=MTczMjQxNjQyNiw4LjIyMi4yMDguMTQ2&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="2792810" href="https://independentresearcher.academia.edu/DrJMAshfaqueAMIMAMInstP">Dr. J. M. Ashfaque (MInstP)</a><script data-card-contents-for-user="2792810" type="text/json">{"id":2792810,"first_name":"Dr. J. M.","last_name":"Ashfaque (MInstP)","domain_name":"independentresearcher","page_name":"DrJMAshfaqueAMIMAMInstP","display_name":"Dr. J. M. 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The Einstein equation for a (d + 2)-dimensional Minkowski-signature space-time with negative cosmological constant is R µν − 1 2 g µν R − d(d + 1) 2L 2 g µν = 0. This is solved by an AdS-Schwarzschild black hole background with the metric ds 2 = r 2 L 2 (−f (r)dt 2 + dΣ 2 k) + L 2 r 2 f (r) dr 2 , i = 1, ..., d where L is the AdS radius and r is the radial direction while f (r) = 1 − m r d+1 +","downloadable_attachments":[{"id":56343277,"asset_id":36429904,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":2792810,"first_name":"Dr. J. M.","last_name":"Ashfaque (MInstP)","domain_name":"independentresearcher","page_name":"DrJMAshfaqueAMIMAMInstP","display_name":"Dr. J. M. Ashfaque (MInstP)","profile_url":"https://independentresearcher.academia.edu/DrJMAshfaqueAMIMAMInstP?f_ri=318","photo":"https://0.academia-photos.com/2792810/914293/18370870/s65_dr._j._m..ashfaque_amima_minstp_.jpg"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":4751,"name":"Black Holes","url":"https://www.academia.edu/Documents/in/Black_Holes?f_ri=318","nofollow":false},{"id":10092,"name":"Quantum Field Theory","url":"https://www.academia.edu/Documents/in/Quantum_Field_Theory?f_ri=318"},{"id":10598,"name":"String Theory","url":"https://www.academia.edu/Documents/in/String_Theory?f_ri=318"},{"id":23179,"name":"Astrophysics","url":"https://www.academia.edu/Documents/in/Astrophysics?f_ri=318"},{"id":47599,"name":"Astronomy","url":"https://www.academia.edu/Documents/in/Astronomy?f_ri=318"},{"id":98734,"name":"AdS/CFT Correspondence","url":"https://www.academia.edu/Documents/in/AdS_CFT_Correspondence?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_33517051" data-work_id="33517051" 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/33517051/Nonlinear_supersymmetry_effective_actions_and_moduli_stabilization">Nonlinear supersymmetry, effective actions and moduli stabilization</a></div></div><div class="u-pb4x 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href="https://www.academia.edu/Documents/in/Pure_Mathematics">Pure Mathematics</a><script data-card-contents-for-ri="19997" type="text/json">{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=26119737]'), work: {"id":26119737,"title":"Reiterated Ergodic Algebras and Applications","created_at":"2016-06-14T00:28:31.631-07:00","url":"https://www.academia.edu/26119737/Reiterated_Ergodic_Algebras_and_Applications?f_ri=318","dom_id":"work_26119737","summary":null,"downloadable_attachments":[{"id":46462243,"asset_id":26119737,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":1670289,"first_name":"Jean Louis","last_name":"Woukeng","domain_name":"univ-dschang","page_name":"JeanLouisWoukeng","display_name":"Jean Louis 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Matter Physics","url":"https://www.academia.edu/Documents/in/Condensed_Matter_Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="71115" href="https://www.academia.edu/Documents/in/Low_Temperature_Physics">Low Temperature Physics</a><script data-card-contents-for-ri="71115" type="text/json">{"id":71115,"name":"Low Temperature Physics","url":"https://www.academia.edu/Documents/in/Low_Temperature_Physics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=25652642]'), work: {"id":25652642,"title":"Superconductors with charge- and spin-density waves: theory and experiment (Review)","created_at":"2016-05-27T04:22:31.634-07:00","url":"https://www.academia.edu/25652642/Superconductors_with_charge_and_spin_density_waves_theory_and_experiment_Review_?f_ri=318","dom_id":"work_25652642","summary":null,"downloadable_attachments":[{"id":45990686,"asset_id":25652642,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":3413987,"first_name":"Alexander","last_name":"Voitenko","domain_name":"iop-kiev","page_name":"AlexanderVoitenko","display_name":"Alexander Voitenko","profile_url":"https://iop-kiev.academia.edu/AlexanderVoitenko?f_ri=318","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":505,"name":"Condensed Matter Physics","url":"https://www.academia.edu/Documents/in/Condensed_Matter_Physics?f_ri=318","nofollow":false},{"id":71115,"name":"Low Temperature 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The new and crucial ingredient is a certain Hopf... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_25506988" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We present the solution of a longstanding internal problem of noncommutative geometry, namely the computation of the index of a transversally elliptic operator on an arbitrary foliation. The new and crucial ingredient is a certain Hopf algebra associated to the transverse frame bundle. Its cyclic cohomology is defined and shown to be canonically isomorphic to the Gelfand-Fuks cohomology.</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/25506988" 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="141f246a1df19ecfc8e00832684e6003" rel="nofollow" data-download="{"attachment_id":45828986,"asset_id":25506988,"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/45828986/download_file?st=MTczMjQxNjQyNiw4LjIyMi4yMDguMTQ2&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="49038361" href="https://independent.academia.edu/AlainConnes">Alain Connes</a><script data-card-contents-for-user="49038361" type="text/json">{"id":49038361,"first_name":"Alain","last_name":"Connes","domain_name":"independent","page_name":"AlainConnes","display_name":"Alain Connes","profile_url":"https://independent.academia.edu/AlainConnes?f_ri=318","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_25506988 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="25506988"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 25506988, container: ".js-paper-rank-work_25506988", }); 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href="https://www.academia.edu/6210031/2012_06_Syntropy_The_New_Thermodynamics_and_Life_Energy">2012-06 Syntropy The New Thermodynamics and Life Energy</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/6210031" 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="5568f7f2c37a7712ae24e325246e9090" rel="nofollow" data-download="{"attachment_id":33083074,"asset_id":6210031,"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 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href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a>, <script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","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=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=6210031]'), work: {"id":6210031,"title":"2012-06 Syntropy The New Thermodynamics and Life Energy","created_at":"2014-02-25T21:38:51.810-08:00","url":"https://www.academia.edu/6210031/2012_06_Syntropy_The_New_Thermodynamics_and_Life_Energy?f_ri=318","dom_id":"work_6210031","summary":null,"downloadable_attachments":[{"id":33083074,"asset_id":6210031,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":9507887,"first_name":"Ulisse","last_name":"Di Corpo","domain_name":"upsol","page_name":"UlisseDiCorpo","display_name":"Ulisse Di Corpo","profile_url":"https://upsol.academia.edu/UlisseDiCorpo?f_ri=318","photo":"https://0.academia-photos.com/9507887/3014336/3540651/s65_ulisse.corpo.png"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=318","nofollow":false},{"id":522,"name":"Thermodynamics","url":"https://www.academia.edu/Documents/in/Thermodynamics?f_ri=318"},{"id":7710,"name":"Biology","url":"https://www.academia.edu/Documents/in/Biology?f_ri=318"},{"id":132094,"name":"Anticipation","url":"https://www.academia.edu/Documents/in/Anticipation?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_6138361" data-work_id="6138361" 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/6138361/Einstein%CA%BCs_Special_Theory_of_Relativity_and_the_Problems_in_the_Electrodynamics_of_Moving_Bodies_that_Led_him_to_it_Prepared_for_Cambridge_Companion_to_Einstein">Einsteinʼs Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies that Led him to it. Prepared for Cambridge Companion to Einstein</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/6138361" 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="81a9ac4515364b1051e1b7caab457f33" rel="nofollow" data-download="{"attachment_id":33035625,"asset_id":6138361,"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/33035625/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="9315534" href="https://kovidrathee.academia.edu/SouravS957">Sourav Surana</a><script data-card-contents-for-user="9315534" type="text/json">{"id":9315534,"first_name":"Sourav","last_name":"Surana","domain_name":"kovidrathee","page_name":"SouravS957","display_name":"Sourav Surana","profile_url":"https://kovidrathee.academia.edu/SouravS957?f_ri=318","photo":"https://0.academia-photos.com/9315534/2982378/3500063/s65_sourav.surana.jpg"}</script></span></span></li><li class="js-paper-rank-work_6138361 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="6138361"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 6138361, container: ".js-paper-rank-work_6138361", }); 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$(".js-view-count[data-work-id=6138361]").text(description); $(".js-view-count-work_6138361").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_6138361").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="6138361"><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="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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a>, <script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="3723" href="https://www.academia.edu/Documents/in/History_of_Science">History of Science</a>, <script data-card-contents-for-ri="3723" type="text/json">{"id":3723,"name":"History of Science","url":"https://www.academia.edu/Documents/in/History_of_Science?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="142804" href="https://www.academia.edu/Documents/in/Einsteins_General_Theory_of_Relativity">Einstein's General Theory of Relativity</a><script data-card-contents-for-ri="142804" type="text/json">{"id":142804,"name":"Einstein's General Theory of Relativity","url":"https://www.academia.edu/Documents/in/Einsteins_General_Theory_of_Relativity?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=6138361]'), work: {"id":6138361,"title":"Einsteinʼs Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies that Led him to it. Prepared for Cambridge Companion to Einstein","created_at":"2014-02-19T14:25:28.456-08:00","url":"https://www.academia.edu/6138361/Einstein%CA%BCs_Special_Theory_of_Relativity_and_the_Problems_in_the_Electrodynamics_of_Moving_Bodies_that_Led_him_to_it_Prepared_for_Cambridge_Companion_to_Einstein?f_ri=318","dom_id":"work_6138361","summary":null,"downloadable_attachments":[{"id":33035625,"asset_id":6138361,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":9315534,"first_name":"Sourav","last_name":"Surana","domain_name":"kovidrathee","page_name":"SouravS957","display_name":"Sourav Surana","profile_url":"https://kovidrathee.academia.edu/SouravS957?f_ri=318","photo":"https://0.academia-photos.com/9315534/2982378/3500063/s65_sourav.surana.jpg"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":3723,"name":"History of Science","url":"https://www.academia.edu/Documents/in/History_of_Science?f_ri=318","nofollow":false},{"id":142804,"name":"Einstein's General Theory of Relativity","url":"https://www.academia.edu/Documents/in/Einsteins_General_Theory_of_Relativity?f_ri=318","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_50953880" data-work_id="50953880" 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/50953880/Spin_statistics_theorem_from_Wightmans_axioms">Spin-statistics theorem from Wightman's axioms</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 quantum mechanics the Pauli exclusion principle plays a crucial role in the description of nature (not least for the explaination of the Mendelejev's table of elements). This principle connects the symmetry or antisymmetry of the N... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_50953880" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In quantum mechanics the Pauli exclusion principle plays a crucial role in the description of nature (not least for the explaination of the Mendelejev's table of elements). This principle connects the symmetry or antisymmetry of the N −particle wave functions of identical particles with the spins, in particular with integer or half-integer spins, respectively. Our pourpose is to discuss the nature of this principle from a QFT point of view, in particular we will prove the Spin-statistics theorem, which is the rigorous statement of the Pauli principle, assuming the Wightman's axioms (to be honest the Wightman axioms for the Wightman's distributions). In order to do that, after a review of theWightaman's axioms, we will discuss first the free case, since this case is somehow special and we don't need many assumptions; then we will discuss the general case.</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/50953880" 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="c59d5199c1d7dee67964b82ee975a3c5" rel="nofollow" data-download="{"attachment_id":69193741,"asset_id":50953880,"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/69193741/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="34076902" href="https://desy.academia.edu/AlessioMiscioscia">Alessio Miscioscia</a><script data-card-contents-for-user="34076902" type="text/json">{"id":34076902,"first_name":"Alessio","last_name":"Miscioscia","domain_name":"desy","page_name":"AlessioMiscioscia","display_name":"Alessio Miscioscia","profile_url":"https://desy.academia.edu/AlessioMiscioscia?f_ri=318","photo":"https://0.academia-photos.com/34076902/29617540/59814341/s65_alessio.miscioscia.jpeg"}</script></span></span></li><li class="js-paper-rank-work_50953880 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="50953880"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 50953880, container: ".js-paper-rank-work_50953880", }); 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$(".js-view-count[data-work-id=50953880]").text(description); $(".js-view-count-work_50953880").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_50953880").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="50953880"><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="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=318","nofollow":false}</script><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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a>, <script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","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=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=50953880]'), work: {"id":50953880,"title":"Spin-statistics theorem from Wightman's axioms","created_at":"2021-08-21T03:41:09.486-07:00","url":"https://www.academia.edu/50953880/Spin_statistics_theorem_from_Wightmans_axioms?f_ri=318","dom_id":"work_50953880","summary":"In quantum mechanics the Pauli exclusion principle plays a crucial role in the description of nature (not least for the explaination of the Mendelejev's table of elements). This principle connects the symmetry or antisymmetry of the N −particle wave functions of identical particles with the spins, in particular with integer or half-integer spins, respectively. Our pourpose is to discuss the nature of this principle from a QFT point of view, in particular we will prove the Spin-statistics theorem, which is the rigorous statement of the Pauli principle, assuming the Wightman's axioms (to be honest the Wightman axioms for the Wightman's distributions). In order to do that, after a review of theWightaman's axioms, we will discuss first the free case, since this case is somehow special and we don't need many assumptions; then we will discuss the general case.","downloadable_attachments":[{"id":69193741,"asset_id":50953880,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":34076902,"first_name":"Alessio","last_name":"Miscioscia","domain_name":"desy","page_name":"AlessioMiscioscia","display_name":"Alessio Miscioscia","profile_url":"https://desy.academia.edu/AlessioMiscioscia?f_ri=318","photo":"https://0.academia-photos.com/34076902/29617540/59814341/s65_alessio.miscioscia.jpeg"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=318","nofollow":false},{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=318","nofollow":false},{"id":10092,"name":"Quantum Field Theory","url":"https://www.academia.edu/Documents/in/Quantum_Field_Theory?f_ri=318"},{"id":97703,"name":"Mathematical Methods of Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Methods_of_Physics?f_ri=318"},{"id":287176,"name":"Axiomatic Method","url":"https://www.academia.edu/Documents/in/Axiomatic_Method?f_ri=318"},{"id":733668,"name":"Spin-Statistics Connection","url":"https://www.academia.edu/Documents/in/Spin-Statistics_Connection?f_ri=318"},{"id":2471733,"name":"Fundations of Quantum Physics","url":"https://www.academia.edu/Documents/in/Fundations_of_Quantum_Physics?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_42782765" data-work_id="42782765" 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/42782765/Vectors_and_Matrices_An_Overview">Vectors and Matrices - An Overview</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/42782765" 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="e3d77aefa4823a98fe30fd3d3e0971c0" rel="nofollow" data-download="{"attachment_id":63007481,"asset_id":42782765,"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/63007481/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="2792810" href="https://independentresearcher.academia.edu/DrJMAshfaqueAMIMAMInstP">Dr. J. M. Ashfaque (MInstP)</a><script data-card-contents-for-user="2792810" type="text/json">{"id":2792810,"first_name":"Dr. J. M.","last_name":"Ashfaque (MInstP)","domain_name":"independentresearcher","page_name":"DrJMAshfaqueAMIMAMInstP","display_name":"Dr. J. M. Ashfaque (MInstP)","profile_url":"https://independentresearcher.academia.edu/DrJMAshfaqueAMIMAMInstP?f_ri=318","photo":"https://0.academia-photos.com/2792810/914293/18370870/s65_dr._j._m..ashfaque_amima_minstp_.jpg"}</script></span></span></li><li class="js-paper-rank-work_42782765 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="42782765"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 42782765, container: ".js-paper-rank-work_42782765", }); });</script></li><li class="js-percentile-work_42782765 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 42782765; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_42782765"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_42782765 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="42782765"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 42782765; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=42782765]").text(description); $(".js-view-count-work_42782765").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_42782765").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="42782765"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">10</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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="305" href="https://www.academia.edu/Documents/in/Applied_Mathematics">Applied Mathematics</a>, <script data-card-contents-for-ri="305" type="text/json">{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=318","nofollow":false}</script><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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="329" href="https://www.academia.edu/Documents/in/Algebra">Algebra</a><script data-card-contents-for-ri="329" type="text/json">{"id":329,"name":"Algebra","url":"https://www.academia.edu/Documents/in/Algebra?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=42782765]'), work: {"id":42782765,"title":"Vectors and Matrices - An Overview","created_at":"2020-04-19T00:30:50.385-07:00","url":"https://www.academia.edu/42782765/Vectors_and_Matrices_An_Overview?f_ri=318","dom_id":"work_42782765","summary":null,"downloadable_attachments":[{"id":63007481,"asset_id":42782765,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":2792810,"first_name":"Dr. J. M.","last_name":"Ashfaque (MInstP)","domain_name":"independentresearcher","page_name":"DrJMAshfaqueAMIMAMInstP","display_name":"Dr. J. M. Ashfaque (MInstP)","profile_url":"https://independentresearcher.academia.edu/DrJMAshfaqueAMIMAMInstP?f_ri=318","photo":"https://0.academia-photos.com/2792810/914293/18370870/s65_dr._j._m..ashfaque_amima_minstp_.jpg"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics?f_ri=318","nofollow":false},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics?f_ri=318","nofollow":false},{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":329,"name":"Algebra","url":"https://www.academia.edu/Documents/in/Algebra?f_ri=318","nofollow":false},{"id":353,"name":"Algebraic Geometry","url":"https://www.academia.edu/Documents/in/Algebraic_Geometry?f_ri=318"},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=318"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics?f_ri=318"},{"id":29972,"name":"Linear Algebra","url":"https://www.academia.edu/Documents/in/Linear_Algebra?f_ri=318"},{"id":63655,"name":"Abstract Algebra","url":"https://www.academia.edu/Documents/in/Abstract_Algebra?f_ri=318"},{"id":247061,"name":"Pure and Applied Mathematics","url":"https://www.academia.edu/Documents/in/Pure_and_Applied_Mathematics?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_42293343" data-work_id="42293343" 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/42293343/AN_APPLICATION_OF_PHYSICS_EXPERIMENTS_OF_HIGH_SCHOOL_BY_USING_AUGMENTED_REALITY">AN APPLICATION OF PHYSICS EXPERIMENTS OF HIGH SCHOOL BY USING AUGMENTED REALITY</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">There has been done little research to validate the utility and usability of virtual and augmented reality environments. The evaluation of usability of these new technologies is very important to design systems that are more intuitive... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_42293343" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">There has been done little research to validate the utility and usability of virtual and augmented reality environments. The evaluation of usability of these new technologies is very important to design systems that are more intuitive than a traditional method. Such an evaluation is also important for future development of applications that can gain from this new technology. The augmented reality (AR) is a technology that embedded virtual object (video, picture and 3D object) to the user view the real world. The combination of AR technology with the educational content creates new type of automated applications and acts to enhance the effectiveness and attractiveness of teaching and learning for students in real life scenarios. The study aims to improve the teaching methods used in secondary school by employing modern educational technology and thus assess the effectiveness of AR apps in teaching students the physics experiments. Therefore, in this study we took the challenge of adapting this technology to facilitate physics subject in secondary school.</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/42293343" 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="0bcec39e9178f3305a3134b112485342" rel="nofollow" data-download="{"attachment_id":62447743,"asset_id":42293343,"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/62447743/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="21169291" href="https://independent.academia.edu/IjseaJournal">International Journal of Software Engineering & Applications (IJSEA)-ERA Indexed</a><script data-card-contents-for-user="21169291" type="text/json">{"id":21169291,"first_name":"International Journal of Software Engineering \u0026 Applications","last_name":"(IJSEA)-ERA Indexed","domain_name":"independent","page_name":"IjseaJournal","display_name":"International Journal of Software Engineering \u0026 Applications (IJSEA)-ERA Indexed","profile_url":"https://independent.academia.edu/IjseaJournal?f_ri=318","photo":"https://0.academia-photos.com/21169291/5886224/84098518/s65_international_journal_of_software_engineering_applications._ijsea_-era_indexed.png"}</script></span></span></li><li class="js-paper-rank-work_42293343 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="42293343"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 42293343, container: ".js-paper-rank-work_42293343", }); 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$(".js-view-count[data-work-id=42293343]").text(description); $(".js-view-count-work_42293343").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_42293343").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="42293343"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">19</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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="498" href="https://www.academia.edu/Documents/in/Physics">Physics</a>, <script data-card-contents-for-ri="498" type="text/json">{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a>, <script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="504" href="https://www.academia.edu/Documents/in/Computational_Physics">Computational Physics</a><script data-card-contents-for-ri="504" type="text/json">{"id":504,"name":"Computational Physics","url":"https://www.academia.edu/Documents/in/Computational_Physics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=42293343]'), work: {"id":42293343,"title":"AN APPLICATION OF PHYSICS EXPERIMENTS OF HIGH SCHOOL BY USING AUGMENTED REALITY","created_at":"2020-03-23T02:49:44.751-07:00","url":"https://www.academia.edu/42293343/AN_APPLICATION_OF_PHYSICS_EXPERIMENTS_OF_HIGH_SCHOOL_BY_USING_AUGMENTED_REALITY?f_ri=318","dom_id":"work_42293343","summary":"There has been done little research to validate the utility and usability of virtual and augmented reality environments. The evaluation of usability of these new technologies is very important to design systems that are more intuitive than a traditional method. Such an evaluation is also important for future development of applications that can gain from this new technology. The augmented reality (AR) is a technology that embedded virtual object (video, picture and 3D object) to the user view the real world. The combination of AR technology with the educational content creates new type of automated applications and acts to enhance the effectiveness and attractiveness of teaching and learning for students in real life scenarios. The study aims to improve the teaching methods used in secondary school by employing modern educational technology and thus assess the effectiveness of AR apps in teaching students the physics experiments. Therefore, in this study we took the challenge of adapting this technology to facilitate physics subject in secondary school.","downloadable_attachments":[{"id":62447743,"asset_id":42293343,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":21169291,"first_name":"International Journal of Software Engineering \u0026 Applications","last_name":"(IJSEA)-ERA Indexed","domain_name":"independent","page_name":"IjseaJournal","display_name":"International Journal of Software Engineering \u0026 Applications (IJSEA)-ERA Indexed","profile_url":"https://independent.academia.edu/IjseaJournal?f_ri=318","photo":"https://0.academia-photos.com/21169291/5886224/84098518/s65_international_journal_of_software_engineering_applications._ijsea_-era_indexed.png"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":504,"name":"Computational Physics","url":"https://www.academia.edu/Documents/in/Computational_Physics?f_ri=318","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=318"},{"id":2151,"name":"Virtual Reality (Computer Graphics)","url":"https://www.academia.edu/Documents/in/Virtual_Reality_Computer_Graphics_?f_ri=318"},{"id":5673,"name":"Augmented Reality","url":"https://www.academia.edu/Documents/in/Augmented_Reality?f_ri=318"},{"id":12697,"name":"Virtual Art \u0026 Virtual Reality","url":"https://www.academia.edu/Documents/in/Virtual_Art_and_Virtual_Reality?f_ri=318"},{"id":12698,"name":"Augmented Reality Art","url":"https://www.academia.edu/Documents/in/Augmented_Reality_Art?f_ri=318"},{"id":17871,"name":"Physics Education","url":"https://www.academia.edu/Documents/in/Physics_Education?f_ri=318"},{"id":24570,"name":"Audio Augmented Reality","url":"https://www.academia.edu/Documents/in/Audio_Augmented_Reality?f_ri=318"},{"id":39369,"name":"Augmented Reality (Computer Science)","url":"https://www.academia.edu/Documents/in/Augmented_Reality_Computer_Science_?f_ri=318"},{"id":41030,"name":"Mobile Augmented Reality","url":"https://www.academia.edu/Documents/in/Mobile_Augmented_Reality?f_ri=318"},{"id":66819,"name":"I+D+I in Augmented Reality","url":"https://www.academia.edu/Documents/in/I_D_I_in_Augmented_Reality?f_ri=318"},{"id":275897,"name":"EDUCATIONAL GAMES, AUGMENTED REALITY, SERIOUS GAMES","url":"https://www.academia.edu/Documents/in/EDUCATIONAL_GAMES_AUGMENTED_REALITY_SERIOUS_GAMES?f_ri=318"},{"id":289031,"name":"Augmented Reality, Education , Mobile application","url":"https://www.academia.edu/Documents/in/Augmented_Reality_Education_Mobile_application?f_ri=318"},{"id":453754,"name":"Augmented and Virtual Reality for Civil and Building Engineering","url":"https://www.academia.edu/Documents/in/Augmented_and_Virtual_Reality_for_Civil_and_Building_Engineering?f_ri=318"},{"id":531041,"name":"Augmented Reality Book","url":"https://www.academia.edu/Documents/in/Augmented_Reality_Book?f_ri=318"},{"id":1019262,"name":"Virtual Reality Technology","url":"https://www.academia.edu/Documents/in/Virtual_Reality_Technology?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_6316128" data-work_id="6316128" 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/6316128/How_does_Europe_Make_Its_Mind_Up_Connections_cliques_and_compatibility_between_countries_in_the_Eurovision_Song_Contest">How does Europe Make Its Mind Up? Connections, cliques, and compatibility between countries in the Eurovision Song Contest</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/6316128" 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="72b81a66f4325a5d9302bf824fa20037" rel="nofollow" data-download="{"attachment_id":48919848,"asset_id":6316128,"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/48919848/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="9819021" href="https://independent.academia.edu/DFenn">Daniel Fenn</a><script data-card-contents-for-user="9819021" type="text/json">{"id":9819021,"first_name":"Daniel","last_name":"Fenn","domain_name":"independent","page_name":"DFenn","display_name":"Daniel Fenn","profile_url":"https://independent.academia.edu/DFenn?f_ri=318","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_6316128 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="6316128"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 6316128, container: ".js-paper-rank-work_6316128", }); 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Connections, cliques, and compatibility between countries in the Eurovision Song Contest","created_at":"2014-03-06T15:19:15.911-08:00","url":"https://www.academia.edu/6316128/How_does_Europe_Make_Its_Mind_Up_Connections_cliques_and_compatibility_between_countries_in_the_Eurovision_Song_Contest?f_ri=318","dom_id":"work_6316128","summary":null,"downloadable_attachments":[{"id":48919848,"asset_id":6316128,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":9819021,"first_name":"Daniel","last_name":"Fenn","domain_name":"independent","page_name":"DFenn","display_name":"Daniel Fenn","profile_url":"https://independent.academia.edu/DFenn?f_ri=318","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=318","nofollow":false},{"id":7125,"name":"Culture","url":"https://www.academia.edu/Documents/in/Culture?f_ri=318","nofollow":false},{"id":54856,"name":"Network Dynamics","url":"https://www.academia.edu/Documents/in/Network_Dynamics?f_ri=318","nofollow":false},{"id":62320,"name":"Dynamics","url":"https://www.academia.edu/Documents/in/Dynamics?f_ri=318"},{"id":84990,"name":"Clustering","url":"https://www.academia.edu/Documents/in/Clustering?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_24498090" data-work_id="24498090" 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/24498090/Entropy_of_Quantum_Black_Holes">Entropy of Quantum 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" data-academia-share="Work/24498090" 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="ebab90b819eae71bdb8806fc49d50ea6" rel="nofollow" data-download="{"attachment_id":44830242,"asset_id":24498090,"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/44830242/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="47139266" href="https://independent.academia.edu/RomeshKaul">Romesh Kaul</a><script data-card-contents-for-user="47139266" type="text/json">{"id":47139266,"first_name":"Romesh","last_name":"Kaul","domain_name":"independent","page_name":"RomeshKaul","display_name":"Romesh Kaul","profile_url":"https://independent.academia.edu/RomeshKaul?f_ri=318","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_24498090 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="24498090"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 24498090, container: ".js-paper-rank-work_24498090", }); 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Volume 1: theory and experiments : Oxford University Press, 2007, 576p., GBP47.00, ISBN13: 978-0-19-857074-5 (Book Review)</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/21096746" 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="dc92feec9758cf5c2a1308482972381f" rel="nofollow" data-download="{"attachment_id":41713067,"asset_id":21096746,"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/41713067/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="411768" href="https://uib-es.academia.edu/SaschaHusa">Sascha Husa</a><script data-card-contents-for-user="411768" type="text/json">{"id":411768,"first_name":"Sascha","last_name":"Husa","domain_name":"uib-es","page_name":"SaschaHusa","display_name":"Sascha Husa","profile_url":"https://uib-es.academia.edu/SaschaHusa?f_ri=318","photo":"https://0.academia-photos.com/411768/129861/149728/s65_sascha.husa.jpg"}</script></span></span></li><li class="js-paper-rank-work_21096746 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="21096746"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 21096746, container: ".js-paper-rank-work_21096746", }); 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$(".js-view-count[data-work-id=20051729]").text(description); $(".js-view-count-work_20051729").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_20051729").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="20051729"><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="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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a><script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=20051729]'), work: {"id":20051729,"title":"Einstein'sThird Postulate","created_at":"2016-01-06T00:45:29.070-08:00","url":"https://www.academia.edu/20051729/EinsteinsThird_Postulate?f_ri=318","dom_id":"work_20051729","summary":null,"downloadable_attachments":[{"id":40978712,"asset_id":20051729,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":41011106,"first_name":"Wolfgang","last_name":"Engelhardt","domain_name":"ipp-mpg","page_name":"WolfgangEngelhardt","display_name":"Wolfgang Engelhardt","profile_url":"https://ipp-mpg.academia.edu/WolfgangEngelhardt?f_ri=318","photo":"https://0.academia-photos.com/41011106/31820301/29039549/s65_wolfgang.engelhardt.jpg"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","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_12284658" data-work_id="12284658" 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/12284658/ANALYSIS_OF_BRAIN_STEM_RESPIRATORY_CENTER_FUNCTION_BY_USE_OF_MATHEMATICAL_APPARATUS_OF_CHAOS_THEORY">ANALYSIS OF BRAIN STEM RESPIRATORY CENTER FUNCTION BY USE OF MATHEMATICAL APPARATUS OF CHAOS THEORY</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">Brain spirography method, that enables recording of slow-wave and fast-wave respiratory curves and analyse them by use of chaos-mathematics, as well as the assessment of the extent of brain energy deficit were used for homeostasis balance... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_12284658" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">Brain spirography method, that enables recording of slow-wave and fast-wave respiratory curves and analyse them by use of chaos-mathematics, as well as the assessment of the extent of brain energy deficit were used for homeostasis balance measurement. 200 patients with ischemic and hemorrhagic stroke were enrolled into the study. On the basis of selected case study, we present an authorial proposal of an algorithm that enables qualitative and quantitative assessment of brain stem homeostasis center function fluctuations, as well as brain energy deficit range evaluation.</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/12284658" 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="8de16b9afda424d74b52ba58da5d247c" rel="nofollow" data-download="{"attachment_id":37573589,"asset_id":12284658,"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/37573589/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="2026063" href="https://wsksim.academia.edu/GrzegorzOsinski">Grzegorz Osinski</a><script data-card-contents-for-user="2026063" type="text/json">{"id":2026063,"first_name":"Grzegorz","last_name":"Osinski","domain_name":"wsksim","page_name":"GrzegorzOsinski","display_name":"Grzegorz Osinski","profile_url":"https://wsksim.academia.edu/GrzegorzOsinski?f_ri=318","photo":"https://0.academia-photos.com/2026063/668003/829177/s65_grzegorz.osinski.jpg"}</script></span></span></li><li class="js-paper-rank-work_12284658 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="12284658"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 12284658, container: ".js-paper-rank-work_12284658", }); 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$(".js-view-count[data-work-id=12284658]").text(description); $(".js-view-count-work_12284658").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_12284658").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="12284658"><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="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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="1210" href="https://www.academia.edu/Documents/in/Informatics">Informatics</a>, <script data-card-contents-for-ri="1210" type="text/json">{"id":1210,"name":"Informatics","url":"https://www.academia.edu/Documents/in/Informatics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="3317" href="https://www.academia.edu/Documents/in/Health_Informatics">Health Informatics</a>, <script data-card-contents-for-ri="3317" type="text/json">{"id":3317,"name":"Health Informatics","url":"https://www.academia.edu/Documents/in/Health_Informatics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="15738" href="https://www.academia.edu/Documents/in/Biomedical_informatics">Biomedical informatics</a><script data-card-contents-for-ri="15738" type="text/json">{"id":15738,"name":"Biomedical informatics","url":"https://www.academia.edu/Documents/in/Biomedical_informatics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=12284658]'), work: {"id":12284658,"title":"ANALYSIS OF BRAIN STEM RESPIRATORY CENTER FUNCTION BY USE OF MATHEMATICAL APPARATUS OF CHAOS THEORY","created_at":"2015-05-07T16:27:14.814-07:00","url":"https://www.academia.edu/12284658/ANALYSIS_OF_BRAIN_STEM_RESPIRATORY_CENTER_FUNCTION_BY_USE_OF_MATHEMATICAL_APPARATUS_OF_CHAOS_THEORY?f_ri=318","dom_id":"work_12284658","summary":"Brain spirography method, that enables recording of slow-wave and fast-wave respiratory curves and analyse them by use of chaos-mathematics, as well as the assessment of the extent of brain energy deficit were used for homeostasis balance measurement. 200 patients with ischemic and hemorrhagic stroke were enrolled into the study. On the basis of selected case study, we present an authorial proposal of an algorithm that enables qualitative and quantitative assessment of brain stem homeostasis center function fluctuations, as well as brain energy deficit range evaluation.","downloadable_attachments":[{"id":37573589,"asset_id":12284658,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":2026063,"first_name":"Grzegorz","last_name":"Osinski","domain_name":"wsksim","page_name":"GrzegorzOsinski","display_name":"Grzegorz Osinski","profile_url":"https://wsksim.academia.edu/GrzegorzOsinski?f_ri=318","photo":"https://0.academia-photos.com/2026063/668003/829177/s65_grzegorz.osinski.jpg"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":1210,"name":"Informatics","url":"https://www.academia.edu/Documents/in/Informatics?f_ri=318","nofollow":false},{"id":3317,"name":"Health Informatics","url":"https://www.academia.edu/Documents/in/Health_Informatics?f_ri=318","nofollow":false},{"id":15738,"name":"Biomedical informatics","url":"https://www.academia.edu/Documents/in/Biomedical_informatics?f_ri=318","nofollow":false},{"id":16682,"name":"Mathematical Modelling","url":"https://www.academia.edu/Documents/in/Mathematical_Modelling?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_11854269" data-work_id="11854269" 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/11854269/Digitales">Digitales</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/11854269" 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="e05ed5d31995d3b75637286a1640c35a" rel="nofollow" data-download="{"attachment_id":37249254,"asset_id":11854269,"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/37249254/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="29265030" href="https://utpl.academia.edu/joseyumizaca">jose yumizaca</a><script data-card-contents-for-user="29265030" type="text/json">{"id":29265030,"first_name":"jose","last_name":"yumizaca","domain_name":"utpl","page_name":"joseyumizaca","display_name":"jose yumizaca","profile_url":"https://utpl.academia.edu/joseyumizaca?f_ri=318","photo":"/images/s65_no_pic.png"}</script></span></span></li><li class="js-paper-rank-work_11854269 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="11854269"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 11854269, container: ".js-paper-rank-work_11854269", }); });</script></li><li class="js-percentile-work_11854269 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 11854269; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_11854269"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_11854269 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="11854269"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 11854269; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=11854269]").text(description); $(".js-view-count-work_11854269").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_11854269").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="11854269"><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="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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a><script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=11854269]'), work: {"id":11854269,"title":"Digitales","created_at":"2015-04-08T12:28:14.612-07:00","url":"https://www.academia.edu/11854269/Digitales?f_ri=318","dom_id":"work_11854269","summary":null,"downloadable_attachments":[{"id":37249254,"asset_id":11854269,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":29265030,"first_name":"jose","last_name":"yumizaca","domain_name":"utpl","page_name":"joseyumizaca","display_name":"jose yumizaca","profile_url":"https://utpl.academia.edu/joseyumizaca?f_ri=318","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","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_11775874" data-work_id="11775874" 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/11775874/The_Continuing_Relevance_of_Lorentz_Ether_Theory_in_the_Age_of_Relativity">The Continuing Relevance of Lorentz Ether Theory in the Age of Relativity</a></div></div><div class="u-pb4x u-mt3x"><div class="summary u-fs14 u-fw300 u-lineHeight1_5 u-tcGrayDarkest"><div class="summarized">With the advent of relativity the Lorentz Ether theory has been relegated to not much more than a historical footnote. What is less well known is that virtually all optical experiments to date to test the validity of special relativity... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_11775874" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">With the advent of relativity the Lorentz Ether theory has been relegated to not much more than a historical footnote. What is less well known is that virtually all optical experiments to date to test the validity of special relativity cannot distinguish between the predicted outcomes of the two theories. We review the historical development of the Lorentz theory as it evolved to address the results of key optical observations of the 19th century. We then examine how modern optical experiments attempting to detect the relative inertial motion of an observer with respect to a preferred reference frame for light remain consistent with Lorentz’s predictions.</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/11775874" 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="2dc3eb6652364c3552d4f48433c4e6d9" rel="nofollow" data-download="{"attachment_id":37196791,"asset_id":11775874,"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/37196791/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="28953162" href="https://independent.academia.edu/DougMarett">Doug Marett</a><script data-card-contents-for-user="28953162" type="text/json">{"id":28953162,"first_name":"Doug","last_name":"Marett","domain_name":"independent","page_name":"DougMarett","display_name":"Doug Marett","profile_url":"https://independent.academia.edu/DougMarett?f_ri=318","photo":"https://0.academia-photos.com/28953162/8237482/9215659/s65_doug.marett.png"}</script></span></span></li><li class="js-paper-rank-work_11775874 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="11775874"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 11775874, container: ".js-paper-rank-work_11775874", }); });</script></li><li class="js-percentile-work_11775874 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 11775874; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_11775874"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_11775874 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="11775874"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 11775874; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=11775874]").text(description); $(".js-view-count-work_11775874").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_11775874").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="11775874"><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="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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a>, <script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="516" href="https://www.academia.edu/Documents/in/Optics">Optics</a>, <script data-card-contents-for-ri="516" type="text/json">{"id":516,"name":"Optics","url":"https://www.academia.edu/Documents/in/Optics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="2035" href="https://www.academia.edu/Documents/in/Relativity">Relativity</a><script data-card-contents-for-ri="2035" type="text/json">{"id":2035,"name":"Relativity","url":"https://www.academia.edu/Documents/in/Relativity?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=11775874]'), work: {"id":11775874,"title":"The Continuing Relevance of Lorentz Ether Theory in the Age of Relativity","created_at":"2015-04-02T21:58:08.508-07:00","url":"https://www.academia.edu/11775874/The_Continuing_Relevance_of_Lorentz_Ether_Theory_in_the_Age_of_Relativity?f_ri=318","dom_id":"work_11775874","summary":"With the advent of relativity the Lorentz Ether theory has been relegated to not much more than a historical footnote. What is less well known is that virtually all optical experiments to date to test the validity of special relativity cannot distinguish between the predicted outcomes of the two theories. We review the historical development of the Lorentz theory as it evolved to address the results of key optical observations of the 19th century. We then examine how modern optical experiments attempting to detect the relative inertial motion of an observer with respect to a preferred reference frame for light remain consistent with Lorentz’s predictions.","downloadable_attachments":[{"id":37196791,"asset_id":11775874,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":28953162,"first_name":"Doug","last_name":"Marett","domain_name":"independent","page_name":"DougMarett","display_name":"Doug Marett","profile_url":"https://independent.academia.edu/DougMarett?f_ri=318","photo":"https://0.academia-photos.com/28953162/8237482/9215659/s65_doug.marett.png"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":516,"name":"Optics","url":"https://www.academia.edu/Documents/in/Optics?f_ri=318","nofollow":false},{"id":2035,"name":"Relativity","url":"https://www.academia.edu/Documents/in/Relativity?f_ri=318","nofollow":false},{"id":47598,"name":"Cosmology","url":"https://www.academia.edu/Documents/in/Cosmology?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_10433344" data-work_id="10433344" 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/10433344/The_variational_method_and_applying_the_perturbation_theory_to_derive_the_Fermi_Dirac_Distribution_Theoretical_Physics_mini_project_I_">The variational method and applying the perturbation theory to derive the Fermi-Dirac Distribution (Theoretical Physics mini-project I)</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 report we examine the importance of different mathematical methods used in physics. Approximation methods such as variational principles are used to attain the ground state energy to a good degree of accuracy, whilst Lagrange... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_10433344" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In this report we examine the importance of different mathematical methods used in    physics. Approximation methods such as variational principles are used to attain the ground state energy to a good degree of accuracy, whilst Lagrange multipliers was used comprehensibly to derive the Fermi-Dirac Distribution in the external reading section.</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/10433344" 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="92465c96a5f06dc7c1e7a2799726b19d" rel="nofollow" data-download="{"attachment_id":36476345,"asset_id":10433344,"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/36476345/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="25593586" href="https://gatech.academia.edu/RahulDass">Rahul K . Dass</a><script data-card-contents-for-user="25593586" type="text/json">{"id":25593586,"first_name":"Rahul","last_name":"Dass","domain_name":"gatech","page_name":"RahulDass","display_name":"Rahul K . Dass","profile_url":"https://gatech.academia.edu/RahulDass?f_ri=318","photo":"https://0.academia-photos.com/25593586/6999933/117606767/s65_rahul.dass.jpg"}</script></span></span></li><li class="js-paper-rank-work_10433344 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="10433344"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 10433344, container: ".js-paper-rank-work_10433344", }); });</script></li><li class="js-percentile-work_10433344 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 10433344; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_10433344"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_10433344 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="10433344"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 10433344; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=10433344]").text(description); $(".js-view-count-work_10433344").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_10433344").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="10433344"><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="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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a><script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=10433344]'), work: {"id":10433344,"title":"The variational method and applying the perturbation theory to derive the Fermi-Dirac Distribution (Theoretical Physics mini-project I)","created_at":"2015-02-01T08:10:05.968-08:00","url":"https://www.academia.edu/10433344/The_variational_method_and_applying_the_perturbation_theory_to_derive_the_Fermi_Dirac_Distribution_Theoretical_Physics_mini_project_I_?f_ri=318","dom_id":"work_10433344","summary":"In this report we examine the importance of different mathematical methods used in physics. Approximation methods such as variational principles are used to attain the ground state energy to a good degree of accuracy, whilst Lagrange multipliers was used comprehensibly to derive the Fermi-Dirac Distribution in the external reading section.","downloadable_attachments":[{"id":36476345,"asset_id":10433344,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":25593586,"first_name":"Rahul","last_name":"Dass","domain_name":"gatech","page_name":"RahulDass","display_name":"Rahul K . Dass","profile_url":"https://gatech.academia.edu/RahulDass?f_ri=318","photo":"https://0.academia-photos.com/25593586/6999933/117606767/s65_rahul.dass.jpg"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","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_10066673 coauthored" data-work_id="10066673" 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/10066673/Simulation_of_trajectory_of_a_point_on_the_surface_of_a_rolling_sphere">Simulation of trajectory of a point on the surface of a rolling sphere</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 wished to determine the trajectory of a point on the circumference, rather in our case, the surface, of a rolling sphere, on a horizontal plane, and thereby simulate it. During rolling, the point of contact between the sphere and the... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_10066673" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">We wished to determine the trajectory of a point on the circumference, rather in our case, the surface, of a rolling sphere, on a horizontal plane, and thereby simulate it. During rolling, the point of contact between the sphere and the surface will be at instantaneous rest. By setting up equations of motion and using Newton’s force and torque expressions and using the rolling condition, we obtained the trajectory of our point, which is a cycloid. By running a program in python, we were able to determine the co-ordinates of our point at any instant of time. We managed to run the simulation on Visual Python. The same problem was then extended to a sphere rolling down an inclined plane and we once again obtained the trajectory of our point as a cycloid.</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/10066673" 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="cb74e01e3a61e72aecabd4dc48fcc9b6" rel="nofollow" data-download="{"attachment_id":36193875,"asset_id":10066673,"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/36193875/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="4472303" href="https://illinois.academia.edu/RohitChandramouli">Rohit S Chandramouli</a><script data-card-contents-for-user="4472303" type="text/json">{"id":4472303,"first_name":"Rohit","last_name":"Chandramouli","domain_name":"illinois","page_name":"RohitChandramouli","display_name":"Rohit S Chandramouli","profile_url":"https://illinois.academia.edu/RohitChandramouli?f_ri=318","photo":"https://0.academia-photos.com/4472303/1833475/9742224/s65_rohit.subbarayan.jpg"}</script></span></span><span class="u-displayInlineBlock InlineList-item-text"> and <span class="u-textDecorationUnderline u-clickable InlineList-item-text js-work-more-authors-10066673">+1</span><div class="hidden js-additional-users-10066673"><div><span itemscope="itemscope" itemprop="author" itemtype="https://schema.org/Person"><a href="https://snu-in.academia.edu/SiddharthSeetharaman">Siddharth Seetharaman</a></span></div></div></span><script>(function(){ var popoverSettings = { el: $('.js-work-more-authors-10066673'), placement: 'bottom', hide_delay: 200, html: true, content: function(){ return $('.js-additional-users-10066673').html(); } } new HoverPopover(popoverSettings); })();</script></li><li class="js-paper-rank-work_10066673 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="10066673"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 10066673, container: ".js-paper-rank-work_10066673", }); });</script></li><li class="js-percentile-work_10066673 InlineList-item InlineList-item--bordered hidden u-tcGrayDark"><span class="percentile-widget hidden"><span class="u-mr2x percentile-widget" style="display: none">•</span><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 10066673; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-percentile-work_10066673"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></li><li class="js-view-count-work_10066673 InlineList-item InlineList-item--bordered hidden"><div><span><span class="js-view-count view-count u-mr2x" data-work-id="10066673"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 10066673; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=10066673]").text(description); $(".js-view-count-work_10066673").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_10066673").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="10066673"><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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="498" href="https://www.academia.edu/Documents/in/Physics">Physics</a>, <script data-card-contents-for-ri="498" type="text/json">{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a>, <script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="504" href="https://www.academia.edu/Documents/in/Computational_Physics">Computational Physics</a><script data-card-contents-for-ri="504" type="text/json">{"id":504,"name":"Computational Physics","url":"https://www.academia.edu/Documents/in/Computational_Physics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=10066673]'), work: {"id":10066673,"title":"Simulation of trajectory of a point on the surface of a rolling sphere","created_at":"2015-01-07T23:57:50.177-08:00","url":"https://www.academia.edu/10066673/Simulation_of_trajectory_of_a_point_on_the_surface_of_a_rolling_sphere?f_ri=318","dom_id":"work_10066673","summary":"We wished to determine the trajectory of a point on the circumference, rather in our case, the surface, of a rolling sphere, on a horizontal plane, and thereby simulate it. During rolling, the point of contact between the sphere and the surface will be at instantaneous rest. By setting up equations of motion and using Newton’s force and torque expressions and using the rolling condition, we obtained the trajectory of our point, which is a cycloid. By running a program in python, we were able to determine the co-ordinates of our point at any instant of time. We managed to run the simulation on Visual Python. The same problem was then extended to a sphere rolling down an inclined plane and we once again obtained the trajectory of our point as a cycloid.\n","downloadable_attachments":[{"id":36193875,"asset_id":10066673,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":4472303,"first_name":"Rohit","last_name":"Chandramouli","domain_name":"illinois","page_name":"RohitChandramouli","display_name":"Rohit S Chandramouli","profile_url":"https://illinois.academia.edu/RohitChandramouli?f_ri=318","photo":"https://0.academia-photos.com/4472303/1833475/9742224/s65_rohit.subbarayan.jpg"},{"id":16858929,"first_name":"Siddharth","last_name":"Seetharaman","domain_name":"snu-in","page_name":"SiddharthSeetharaman","display_name":"Siddharth Seetharaman","profile_url":"https://snu-in.academia.edu/SiddharthSeetharaman?f_ri=318","photo":"/images/s65_no_pic.png"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":504,"name":"Computational Physics","url":"https://www.academia.edu/Documents/in/Computational_Physics?f_ri=318","nofollow":false},{"id":515,"name":"Newtonian Dynamics","url":"https://www.academia.edu/Documents/in/Newtonian_Dynamics?f_ri=318"},{"id":18996,"name":"Experimental Physics","url":"https://www.academia.edu/Documents/in/Experimental_Physics?f_ri=318"},{"id":158331,"name":"Python Programming","url":"https://www.academia.edu/Documents/in/Python_Programming?f_ri=318"},{"id":442067,"name":"Classical Mechanics","url":"https://www.academia.edu/Documents/in/Classical_Mechanics?f_ri=318"},{"id":921637,"name":"Rolling","url":"https://www.academia.edu/Documents/in/Rolling?f_ri=318"}]}, }) } })();</script></ul></li></ul></div></div><div class="u-borderBottom1 u-borderColorGrayLighter"><div class="clearfix u-pv7x u-mb0x js-work-card work_9292271" data-work_id="9292271" 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/9292271/EM_3_Section_3_Gauss_Law_3_1_Conductors_and_Insulators">EM 3 Section 3: Gauss' Law 3. 1. Conductors and Insulators</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/9292271" 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="6d160433bcde647cb7d30df29a2f7362" rel="nofollow" data-download="{"attachment_id":35554370,"asset_id":9292271,"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/35554370/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="21404807" href="https://unajni.academia.edu/AdhaFadhilMochammad">Adha Fadhil Mochammad</a><script data-card-contents-for-user="21404807" type="text/json">{"id":21404807,"first_name":"Adha","last_name":"Fadhil Mochammad","domain_name":"unajni","page_name":"AdhaFadhilMochammad","display_name":"Adha Fadhil Mochammad","profile_url":"https://unajni.academia.edu/AdhaFadhilMochammad?f_ri=318","photo":"https://0.academia-photos.com/21404807/6113105/6930816/s65_adha.fadhil_mochammad.jpg_oh_04034b7ece710f9ba185f22566beeae3_oe_550c2036___gda___1427157899_7df824793226208288f2e66239d9e449"}</script></span></span></li><li class="js-paper-rank-work_9292271 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="9292271"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 9292271, container: ".js-paper-rank-work_9292271", }); 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$(".js-view-count[data-work-id=9292271]").text(description); $(".js-view-count-work_9292271").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_9292271").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="9292271"><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="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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a>, <script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","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=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=9292271]'), work: {"id":9292271,"title":"EM 3 Section 3: Gauss' Law 3. 1. Conductors and Insulators","created_at":"2014-11-13T08:54:15.944-08:00","url":"https://www.academia.edu/9292271/EM_3_Section_3_Gauss_Law_3_1_Conductors_and_Insulators?f_ri=318","dom_id":"work_9292271","summary":null,"downloadable_attachments":[{"id":35554370,"asset_id":9292271,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":21404807,"first_name":"Adha","last_name":"Fadhil Mochammad","domain_name":"unajni","page_name":"AdhaFadhilMochammad","display_name":"Adha Fadhil Mochammad","profile_url":"https://unajni.academia.edu/AdhaFadhilMochammad?f_ri=318","photo":"https://0.academia-photos.com/21404807/6113105/6930816/s65_adha.fadhil_mochammad.jpg_oh_04034b7ece710f9ba185f22566beeae3_oe_550c2036___gda___1427157899_7df824793226208288f2e66239d9e449"}],"research_interests":[{"id":318,"name":"Mathematical Physics","url":"https://www.academia.edu/Documents/in/Mathematical_Physics?f_ri=318","nofollow":false},{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false},{"id":518,"name":"Quantum Physics","url":"https://www.academia.edu/Documents/in/Quantum_Physics?f_ri=318","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_8855493" data-work_id="8855493" 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/8855493/The_Interdependence_of_Math_and_Physics_in_Early_Attempts_to_Generalize_World_Geometry">The Interdependence of Math and Physics in Early Attempts to Generalize World Geometry</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 1915, Einstein introduced a radical and revolutionary new idea into science and human thought: Gravity was not a force. The observed gravitational attraction between two or more material bodies was the product of the material bodies... <a class="more_link u-tcGrayDark u-linkUnstyled" data-container=".work_8855493" data-show=".complete" data-hide=".summarized" data-more-link-behavior="true" href="#">more</a></div><div class="complete hidden">In 1915, Einstein introduced a radical and revolutionary new idea into science and human thought: Gravity was not a force. The observed gravitational attraction between two or more material bodies was the product of the material bodies following the shortest geodesic paths across the curvature of a space-time continuum. The amount or degree of curvature at any location depended on the local presence of matter. As radical as this idea was, the theory became a known and accepted part of physics within just a few years, which was quite rapid relative to the overall scale of changes in science. It was accepted so rapidly because a few scientists had been attempting to find a connection between non-Euclidean geometry (especially Riemannian) and physics for several decades as well as how the geometry of space (or space-time) was related to ultimate nature and structure of matter. However, Einstein’s theory also came as a surprise because no one had detected any specific flaw in Newtonian gravity theory and other researchers working on the problem of matter had expected matter to ultimately be electric (electromagnetic) in nature. Within this historical context, several scientists and mathematicians immediately noticed a problem with the new theory and took advantage of that problem to extend physics further than Einstein originally anticipated. Although a tensor placed at a point in space was used to represent the curvature through that point, the mathematics and physics at the point itself was not completely specified or explained. This flaw allowed others to develop non-Riemannian and pseudo-Riemannian geometries (also called tangent spaces) to explain geometry specifically at or in the individual points of space-time. Since they were independent of the Riemannian metric geometry of extended (metric) space, these new geometries could be used to explain the electromagnetic nature of matter without disturbing the metric or gravitational explanation given by general relativity. This not only began the search for a unified field theory, but it also demonstrated quite clearly that the attempted rigorization of mathematics that had occurred over the past two centuries was inadequate and mathematics was still intimately linked to physics. The story of how these new geometries developed is both interesting and intriguing, yet so much more. The development of physics over the next few decades cannot be completely understood without taking these events into account. This lost history explains fully both Einstein’s search for a unified field theory (with an emphasis on a metric or extension geometry) as well as the later development of quantum mechanics based on the uncertainty principle and how that relates to quantum field theories (using a point non-geometrical space or space-time), thus changing the whole historical context of modern physics.</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/8855493" 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="0d255b4057408fc6ae1446b15f972dad" rel="nofollow" data-download="{"attachment_id":35192542,"asset_id":8855493,"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/35192542/download_file?st=MTczMjQxNjQyNyw4LjIyMi4yMDguMTQ2&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="13393868" href="https://webplus.academia.edu/JamesJimBeichler">James (Jim) E Beichler</a><script data-card-contents-for-user="13393868" type="text/json">{"id":13393868,"first_name":"James (Jim)","last_name":"Beichler","domain_name":"webplus","page_name":"JamesJimBeichler","display_name":"James (Jim) E Beichler","profile_url":"https://webplus.academia.edu/JamesJimBeichler?f_ri=318","photo":"https://0.academia-photos.com/13393868/3842772/4496298/s65_jim.beichler.jpg"}</script></span></span></li><li class="js-paper-rank-work_8855493 InlineList-item InlineList-item--bordered hidden"><span class="js-paper-rank-view hidden u-tcGrayDark" data-paper-rank-work-id="8855493"><i class="u-m1x fa fa-bar-chart"></i><strong class="js-paper-rank"></strong></span><script>$(function() { new Works.PaperRankView({ workId: 8855493, container: ".js-paper-rank-work_8855493", }); 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$(".js-view-count[data-work-id=8855493]").text(description); $(".js-view-count-work_8855493").attr('title', description).tooltip(); }); });</script></span><script>$(function() { $(".js-view-count-work_8855493").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="8855493"><i class="fa fa-tag InlineList-item-icon u-positionRelative"></i>  <a class="InlineList-item-text u-positionRelative">35</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=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="357" href="https://www.academia.edu/Documents/in/Non_Euclidean_Geometry">Non Euclidean Geometry</a>, <script data-card-contents-for-ri="357" type="text/json">{"id":357,"name":"Non Euclidean Geometry","url":"https://www.academia.edu/Documents/in/Non_Euclidean_Geometry?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="498" href="https://www.academia.edu/Documents/in/Physics">Physics</a>, <script data-card-contents-for-ri="498" type="text/json">{"id":498,"name":"Physics","url":"https://www.academia.edu/Documents/in/Physics?f_ri=318","nofollow":false}</script><a class="InlineList-item-text" data-has-card-for-ri="503" href="https://www.academia.edu/Documents/in/Theoretical_Physics">Theoretical Physics</a><script data-card-contents-for-ri="503" type="text/json">{"id":503,"name":"Theoretical Physics","url":"https://www.academia.edu/Documents/in/Theoretical_Physics?f_ri=318","nofollow":false}</script></span></li><script>(function(){ if (true) { new Aedu.ResearchInterestListCard({ el: $('*[data-has-card-for-ri-list=8855493]'), work: {"id":8855493,"title":"The Interdependence of Math and Physics in Early Attempts to Generalize World Geometry","created_at":"2014-10-19T10:29:21.431-07:00","url":"https://www.academia.edu/8855493/The_Interdependence_of_Math_and_Physics_in_Early_Attempts_to_Generalize_World_Geometry?f_ri=318","dom_id":"work_8855493","summary":"In 1915, Einstein introduced a radical and revolutionary new idea into science and human thought: Gravity was not a force. The observed gravitational attraction between two or more material bodies was the product of the material bodies following the shortest geodesic paths across the curvature of a space-time continuum. The amount or degree of curvature at any location depended on the local presence of matter. As radical as this idea was, the theory became a known and accepted part of physics within just a few years, which was quite rapid relative to the overall scale of changes in science. It was accepted so rapidly because a few scientists had been attempting to find a connection between non-Euclidean geometry (especially Riemannian) and physics for several decades as well as how the geometry of space (or space-time) was related to ultimate nature and structure of matter. However, Einstein’s theory also came as a surprise because no one had detected any specific flaw in Newtonian gravity theory and other researchers working on the problem of matter had expected matter to ultimately be electric (electromagnetic) in nature. Within this historical context, several scientists and mathematicians immediately noticed a problem with the new theory and took advantage of that problem to extend physics further than Einstein originally anticipated. Although a tensor placed at a point in space was used to represent the curvature through that point, the mathematics and physics at the point itself was not completely specified or explained. This flaw allowed others to develop non-Riemannian and pseudo-Riemannian geometries (also called tangent spaces) to explain geometry specifically at or in the individual points of space-time. Since they were independent of the Riemannian metric geometry of extended (metric) space, these new geometries could be used to explain the electromagnetic nature of matter without disturbing the metric or gravitational explanation given by general relativity. This not only began the search for a unified field theory, but it also demonstrated quite clearly that the attempted rigorization of mathematics that had occurred over the past two centuries was inadequate and mathematics was still intimately linked to physics. The story of how these new geometries developed is both interesting and intriguing, yet so much more. The development of physics over the next few decades cannot be completely understood without taking these events into account. This lost history explains fully both Einstein’s search for a unified field theory (with an emphasis on a metric or extension geometry) as well as the later development of quantum mechanics based on the uncertainty principle and how that relates to quantum field theories (using a point non-geometrical space or space-time), thus changing the whole historical context of modern physics.\r\n","downloadable_attachments":[{"id":35192542,"asset_id":8855493,"asset_type":"Work","always_allow_download":false}],"ordered_authors":[{"id":13393868,"first_name":"James (Jim)","last_name":"Beichler","domain_name":"webplus","page_name":"JamesJimBeichler","display_name":"James (Jim) E Beichler","profile_url":"https://webplus.academia.edu/JamesJimBeichler?f_ri=318","photo":"https://0.academia-photos.com/13393868/3842772/4496298/s65_jim.beichler.jpg"}],"research_interests":[{"id":318,"name":"Mathematical 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