{"id":1327,"date":"2025-08-08T15:02:37","date_gmt":"2025-08-08T15:02:37","guid":{"rendered":"https:\/\/projects.ift.uam-csic.es\/master\/?p=1327"},"modified":"2026-07-17T10:49:40","modified_gmt":"2026-07-17T10:49:40","slug":"advanced-quantum-field-theory-aqft","status":"publish","type":"post","link":"https:\/\/projects.ift.uam-csic.es\/master\/advanced-quantum-field-theory-aqft\/","title":{"rendered":"Advanced Quantum Field Theory (AQFT)"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; _builder_version=&#8221;4.27.4&#8243; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row _builder_version=&#8221;4.16&#8243; background_size=&#8221;initial&#8221; background_position=&#8221;top_left&#8221; background_repeat=&#8221;repeat&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.16&#8243; custom_padding=&#8221;|||&#8221; global_colors_info=&#8221;{}&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Academic Team<\/h2>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-41-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (41)&#8221; _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; hover_enabled=&#8221;0&#8243; global_colors_info=&#8221;{}&#8221; url=&#8221;https:\/\/portalcientifico.uam.es\/es\/ipublic\/researcher\/264653&#8243; url_new_window=&#8221;on&#8221; sticky_enabled=&#8221;0&#8243;][\/et_pb_image][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Course Content<\/h2>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<p><strong>Type: Optional\u2013 PEC Track \u2013 2nd Trimeste<\/strong>r<\/p>\n<p>This advanced Quantum Field Theory (QFT) course focuses on the<span>\u00a0<\/span><strong>path integral formulation<\/strong> as a unifying framework to describe and compute physical processes in high-energy physics. The course builds a deep understanding of <strong>renormalization<\/strong> in QFT, with a strong emphasis on <strong>gauge theories<\/strong>\u2014both abelian (QED) and non-abelian (QCD). Students will develop technical skills to derive Feynman rules from the path integral, calculate loop corrections, and analyze the behavior of couplings via <strong>Renormalization Group (RG)<\/strong> equations.<\/p>\n<p>A significant part of the course is devoted to the <strong>spontaneous breaking of symmetries<\/strong>\u2014both global and local\u2014and the <strong>Higgs mechanism<\/strong>, providing the theoretical foundation for the mass generation of gauge bosons in the Standard Model. By the end of the course, students will be equipped with the mathematical and conceptual tools needed for cutting-edge research in theoretical particle physics and related fields.<\/p>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Reading List<\/h2>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<ul>\n<li>T. Banks,<span>\u00a0<\/span><em>Modern Quantum Field Theory: A Concise Introduction<\/em>, Cambridge University Press.<\/li>\n<li>M. Peskin &amp; D. Schroeder,<span>\u00a0<\/span><em>An Introduction to Quantum Field Theory<\/em>, Addison-Wesley.<\/li>\n<li>M. Srednicki,<span>\u00a0<\/span><em>Quantum Field Theory<\/em>, Cambridge University Press.<\/li>\n<li>S. Weinberg,<span>\u00a0<\/span><em>The Quantum Theory of Fields<\/em>, Vols. I &amp; II, Cambridge University Press.<\/li>\n<li>A. Zee,<span>\u00a0<\/span><em>Quantum Field Theory in a Nutshell<\/em>, Princeton University Press.<\/li>\n<li>J. Collins,<span>\u00a0<\/span><em>Renormalization<\/em>, Cambridge Monographs on Mathematical Physics.<\/li>\n<li>M. D. Schwartz,<span>\u00a0<\/span><em>Quantum Field Theory and the Standard Model<\/em>, Cambridge University Press.<\/li>\n<\/ul>\n<p>[\/et_pb_text][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Teaching Plan Information<\/h2>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (21)&#8221; url=&#8221;https:\/\/drive.google.com\/file\/d\/1A9sAQdsDmyDm9nx3G7N9ZQEJW9CKE9Uf\/view&#8221; url_new_window=&#8221;on&#8221; _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; width=&#8221;50%&#8221; max_width=&#8221;50%&#8221; module_alignment=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][et_pb_text _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; header_2_font_size=&#8221;30px&#8221; custom_margin=&#8221;50px||||false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Course Schedule<\/h2>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (20)&#8221; url_new_window=&#8221;on&#8221; _builder_version=&#8221;4.27.4&#8243; _module_preset=&#8221;default&#8221; width=&#8221;50%&#8221; max_width=&#8221;50%&#8221; module_alignment=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Academic TeamCourse ContentType: Optional\u2013 PEC Track \u2013 2nd Trimester This advanced Quantum Field Theory (QFT) course focuses on the\u00a0path integral formulation as a unifying framework to describe and compute physical processes in high-energy physics. The course builds a deep understanding of renormalization in QFT, with a strong emphasis on gauge theories\u2014both abelian (QED) and non-abelian [&hellip;]<\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Academic Team<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:image {\"lightbox\":{\"enabled\":false},\"id\":1494,\"sizeSlug\":\"large\",\"linkDestination\":\"custom\"} -->\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/portalcientifico.uam.es\/es\/ipublic\/researcher\/264653\"><img src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-41-1024x576.png\" alt=\"\" class=\"wp-image-1494\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p><strong>Type: Optional\u2013 PEC Track \u2013 2nd Trimeste<\/strong>r<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>This advanced Quantum Field Theory (QFT) course focuses on the <strong>path integral formulation<\/strong> as a unifying framework to describe and compute physical processes in high-energy physics. The course builds a deep understanding of <strong>renormalization<\/strong> in QFT, with a strong emphasis on <strong>gauge theories<\/strong>\u2014both abelian (QED) and non-abelian (QCD). Students will develop technical skills to derive Feynman rules from the path integral, calculate loop corrections, and analyze the behavior of couplings via <strong>Renormalization Group (RG)<\/strong> equations.<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>A significant part of the course is devoted to the <strong>spontaneous breaking of symmetries<\/strong>\u2014both global and local\u2014and the <strong>Higgs mechanism<\/strong>, providing the theoretical foundation for the mass generation of gauge bosons in the Standard Model. By the end of the course, students will be equipped with the mathematical and conceptual tools needed for cutting-edge research in theoretical particle physics and related fields.<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Reading List<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:list -->\n<ul class=\"wp-block-list\"><!-- wp:list-item -->\n<li>T. Banks, <em>Modern Quantum Field Theory: A Concise Introduction<\/em>, Cambridge University Press.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>M. Peskin &amp; D. Schroeder, <em>An Introduction to Quantum Field Theory<\/em>, Addison-Wesley.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>M. Srednicki, <em>Quantum Field Theory<\/em>, Cambridge University Press.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>S. Weinberg, <em>The Quantum Theory of Fields<\/em>, Vols. I &amp; II, Cambridge University Press.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>A. Zee, <em>Quantum Field Theory in a Nutshell<\/em>, Princeton University Press.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>J. Collins, <em>Renormalization<\/em>, Cambridge Monographs on Mathematical Physics.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li>M. D. Schwartz, <em>Quantum Field Theory and the Standard Model<\/em>, Cambridge University Press.<\/li>\n<!-- \/wp:list-item --><\/ul>\n<!-- \/wp:list -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Teaching Plan Information<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:image {\"lightbox\":{\"enabled\":false},\"id\":1470,\"width\":\"420px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"custom\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><a href=\"https:\/\/drive.google.com\/file\/d\/1A9sAQdsDmyDm9nx3G7N9ZQEJW9CKE9Uf\/view?usp=drive_link\"><img src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-21-3-1024x576.png\" alt=\"\" class=\"wp-image-1470\" style=\"width:420px;height:auto\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Course Schedule<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:image {\"id\":1471,\"width\":\"368px\",\"height\":\"auto\",\"sizeSlug\":\"large\",\"linkDestination\":\"none\",\"align\":\"center\"} -->\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-20-4-1024x576.png\" alt=\"\" class=\"wp-image-1471\" style=\"width:368px;height:auto\"\/><\/figure>\n<!-- \/wp:image -->","_et_gb_content_width":"1080","footnotes":""},"categories":[26,22],"tags":[],"class_list":["post-1327","post","type-post","status-publish","format-standard","hentry","category-optional-en","category-pec-track"],"_links":{"self":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1327","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/comments?post=1327"}],"version-history":[{"count":7,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1327\/revisions"}],"predecessor-version":[{"id":2372,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1327\/revisions\/2372"}],"wp:attachment":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/media?parent=1327"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/categories?post=1327"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/tags?post=1327"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}