{"id":20978,"date":"2018-03-09T09:10:33","date_gmt":"2018-03-09T09:10:33","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/clifford-algebra-in-general-relativity-and-higher-dimensions\/"},"modified":"2018-03-09T09:10:33","modified_gmt":"2018-03-09T09:10:33","slug":"clifford-algebra-in-general-relativity-and-higher-dimensions","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/fisica\/clifford-algebra-in-general-relativity-and-higher-dimensions\/","title":{"rendered":"Clifford algebra in general relativity and higher dimensions"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jos\u00e9 M. Pozo Soler <\/strong><\/h2>\n<p>Las formas diferenciales y el c\u00e1lculo tensorial est\u00e1ndar son dos sistemas matem\u00e1ticos complementarios, b\u00e1sicos en la teoria de la relatividad general y en muchas otras teor\u00edas f\u00edsicas. En esta tesis se presenta el \u00e1lgebra de clifford como una tercera herramienta matem\u00e1tica, \u00fatil en los c\u00e1lculos y razonamientos que involucran campos tensoriales, complementando tanto el c\u00e1lculo tensorial como el de formas exteriores. La estructuraci\u00f3n de los tensores como multivectores r-fold es siempre posible y constituye la estructura base sobre la cual se define el \u00e1lgebra r-fold de clifford, y que reune conceptos propios de los tres sistemas.  la tesis presenta dos aplicaciones de esta estructura de marcado inter\u00e9s f\u00edsico. La primera es la clasificaci\u00f3n de petrov del tensor conforme de weyl. Se obtiene una generalizaci\u00f3n de la identidad de lanczos v\u00e1lida para dimensi\u00f3n par y se introduce un m\u00e9todo original para la clasificaci\u00f3n del tensor de weyl en dimensi\u00f3n 6. Se estudian las propiedades b\u00e1sicas de esta clasificaci\u00f3n en cada una de las posibles signaturas.  la segunda aplicaci\u00f3n parte de la reformulaci\u00f3n del proceso alg\u00e9brico introducido por senovilla para la definici\u00f3n de tensores de superenerg\u00eda. El \u00e1lgebra r-fold de clifford permite una remarcable simplificaci\u00f3n en su expresi\u00f3n y en la demostraci\u00f3n de su positividad, y la obtenci\u00f3n de resultados nuevos importantes en relaci\u00f3n a sus propiedades de conservaci\u00f3n local y de simetr\u00eda. tambi\u00e9n se obtiene una generalizaci\u00f3n del concepto de direcciones is\u00f3tropas principales.  la tesis tambi\u00e9n presenta una clasificaci\u00f3n completa de la descomposici\u00f3n, invariante para el grupo ortogonal, de los dobles multivectores, basada en las funciones internas de traza y cotraza. Diversas identidades son obtenidas, entre ellas la precursora de la generalizaci\u00f3n de la identidad de lanczos.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Clifford algebra in general relativity and higher dimensions<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Clifford algebra in general relativity and higher dimensions <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jos\u00e9 M. Pozo Soler <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 20\/12\/2002<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li> Parra Serra Josep Manel<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jos\u00e9 Mar\u00eda Mart\u00edn senovilla <\/li>\n<li>bartolom\u00e9 Coll (vocal)<\/li>\n<li>garret Sobczyk (vocal)<\/li>\n<li>xavier Jaen herrera (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jos\u00e9 M. Pozo Soler Las formas diferenciales y el c\u00e1lculo tensorial est\u00e1ndar son dos sistemas matem\u00e1ticos complementarios, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[951,199,1432,2855,5766],"tags":[63560,63561,63558,5770,63559,63562],"class_list":["post-20978","post","type-post","status-publish","format-standard","hentry","category-barcelona","category-fisica","category-fisica-teorica","category-teoria-de-la-gravitacion-universal","category-teoria-de-la-relatividad","tag-bartolome-coll","tag-garret-sobczyk","tag-jose-m-pozo-soler","tag-jose-maria-martin-senovilla","tag-parra-serra-josep-manel","tag-xavier-jaen-herrera"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/20978","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=20978"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/20978\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=20978"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=20978"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=20978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}