{"id":1318,"date":"2025-08-08T14:48:03","date_gmt":"2025-08-08T14:48:03","guid":{"rendered":"https:\/\/projects.ift.uam-csic.es\/master\/?p=1318"},"modified":"2026-07-17T10:40:38","modified_gmt":"2026-07-17T10:40:38","slug":"quantum-field-theory-qft","status":"publish","type":"post","link":"https:\/\/projects.ift.uam-csic.es\/master\/quantum-field-theory-qft\/","title":{"rendered":"Quantum Field Theory (QFT)"},"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-46-scaled.png&#8221; title_text=&#8221;Asignaturas m\u00e1ster (46)&#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:\/\/members.ift.uam-csic.es\/cpena\/&#8221; 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: Compulsory\u2013 PEC Track \u2013 1st Trimeste<\/strong>r<\/p>\n<p>This course introduces<span>\u00a0<\/span><strong>Quantum Field Theory (QFT)<\/strong><span>\u00a0<\/span>in the operator formalism, providing the essential tools to describe interactions among elementary particles. Beginning with the quantization of scalar and spinor fields, students progress to<span>\u00a0<\/span><strong>Quantum Electrodynamics (QED)<\/strong>, symmetry principles, and an introduction to non-abelian gauge theories. The course blends conceptual foundations with practical computational techniques, including Feynman diagrams, scattering amplitudes, and renormalization.<\/p>\n<p><strong>Main Topics<\/strong><\/p>\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><strong>Foundations of QFT<\/strong> \u2013 Motivation, connection between quantum mechanics and special relativity, spin\u2013statistics, locality, and causality.<\/li>\n<li><strong>Scalar Fields<\/strong> \u2013 Canonical quantization, propagators, vacuum energy, Casimir effect, and interactions in scalar theories (\u03bb\u03d5\u2074, Yukawa).<\/li>\n<li><strong>Spinor Fields<\/strong> \u2013 Dirac and Weyl equations, chirality, Majorana fermions, fermion quantization, and Feynman rules for fermions.<\/li>\n<li><strong>Quantum Electrodynamics (QED)<\/strong> \u2013 Gauge invariance, quantization of the electromagnetic field, QED Feynman rules, key scattering processes (Bhabha, Compton), and loop corrections.<\/li>\n<li><strong>Renormalization<\/strong> \u2013 Power counting, divergences, dimensional regularization, and electron self-energy.<\/li>\n<li><strong>Non-Abelian Gauge Theories<\/strong><span>\u00a0<\/span>\u2013 Lagrangians for gauge fields and fermions, gauge invariance, running couplings, and asymptotic freedom.<\/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>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><em>An Introduction to Quantum Field Theory<\/em>, M.E. Peskin and D.V. Schroeder. Addison-Wesley Pub. Co. (1995).<\/li>\n<li><em>The Quantum Theory of Fields<\/em>, Vols. I and II, S. Weinberg. Cambridge Univ Press (1995). Curso 2018-2019.<\/li>\n<li><em>Quantum Field Theory in a Nutshell<\/em>, A. Zee. Princeton University (2003).<\/li>\n<li><em>Quantum Field Theory<\/em>, M. Srednicki. Cambridge Univ Press (2007).<\/li>\n<li><em>Modern Quantum Field Theory<\/em>, T. Banks. Cambridge Univ Press (2008).<\/li>\n<li><em>Quantum Field Theory<\/em>, C. Itzykson and J.B. Zuber. McGraw Hill (1980).<\/li>\n<li><em>Field Theory: a Modern Primer<\/em>, P. Ramond. Benjamin (1981).<\/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>Course Outline<\/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\/1ta8gjgNkhOK7tW6oFdWArc_nE3TdKWQg\/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=&#8221;https:\/\/drive.google.com\/file\/d\/1r-RhyerqIKhD8OiP9Du36V49t8MW_oBz\/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_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Academic TeamCourse ContentType: Compulsory\u2013 PEC Track \u2013 1st Trimester This course introduces\u00a0Quantum Field Theory (QFT)\u00a0in the operator formalism, providing the essential tools to describe interactions among elementary particles. Beginning with the quantization of scalar and spinor fields, students progress to\u00a0Quantum Electrodynamics (QED), symmetry principles, and an introduction to non-abelian gauge theories. The course blends conceptual [&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\":1505,\"sizeSlug\":\"large\",\"linkDestination\":\"custom\"} -->\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/members.ift.uam-csic.es\/cpena\/\"><img src=\"https:\/\/projects.ift.uam-csic.es\/master\/wp-content\/uploads\/2025\/08\/Asignaturas-master-46-1024x576.png\" alt=\"\" class=\"wp-image-1505\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Course Content<\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:paragraph -->\n<p><strong>Type: Compulsory\u2013 PEC Track \u2013 1st Trimeste<\/strong>r<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p>This course introduces <strong>Quantum Field Theory (QFT)<\/strong> in the operator formalism, providing the essential tools to describe interactions among elementary particles. Beginning with the quantization of scalar and spinor fields, students progress to <strong>Quantum Electrodynamics (QED)<\/strong>, symmetry principles, and an introduction to non-abelian gauge theories. The course blends conceptual foundations with practical computational techniques, including Feynman diagrams, scattering amplitudes, and renormalization.<\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:paragraph -->\n<p><strong>Main Topics<\/strong><\/p>\n<!-- \/wp:paragraph -->\n\n<!-- wp:list -->\n<ul class=\"wp-block-list\"><!-- wp:list-item -->\n<li><strong>Foundations of QFT<\/strong> \u2013 Motivation, connection between quantum mechanics and special relativity, spin\u2013statistics, locality, and causality.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><strong>Scalar Fields<\/strong> \u2013 Canonical quantization, propagators, vacuum energy, Casimir effect, and interactions in scalar theories (\u03bb\u03d5\u2074, Yukawa).<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><strong>Spinor Fields<\/strong> \u2013 Dirac and Weyl equations, chirality, Majorana fermions, fermion quantization, and Feynman rules for fermions.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><strong>Quantum Electrodynamics (QED)<\/strong> \u2013 Gauge invariance, quantization of the electromagnetic field, QED Feynman rules, key scattering processes (Bhabha, Compton), and loop corrections.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><strong>Renormalization<\/strong> \u2013 Power counting, divergences, dimensional regularization, and electron self-energy.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><strong>Non-Abelian Gauge Theories<\/strong> \u2013 Lagrangians for gauge fields and fermions, gauge invariance, running couplings, and asymptotic freedom.<\/li>\n<!-- \/wp:list-item --><\/ul>\n<!-- \/wp:list -->\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><em>An Introduction to Quantum Field Theory<\/em>, M.E. Peskin and D.V. Schroeder. Addison-Wesley Pub. Co. (1995).<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>The Quantum Theory of Fields<\/em>, Vols. I and II, S. Weinberg. Cambridge Univ Press (1995). Curso 2018-2019.<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>Quantum Field Theory in a Nutshell<\/em>, A. Zee. Princeton University (2003).<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>Quantum Field Theory<\/em>, M. Srednicki. Cambridge Univ Press (2007).<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>Modern Quantum Field Theory<\/em>, T. Banks. Cambridge Univ Press (2008).<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>Quantum Field Theory<\/em>, C. Itzykson and J.B. Zuber. McGraw Hill (1980).<\/li>\n<!-- \/wp:list-item -->\n\n<!-- wp:list-item -->\n<li><em>Field Theory: a Modern Primer<\/em>, P. Ramond. Benjamin (1981).<\/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\":\"355px\",\"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\/1ta8gjgNkhOK7tW6oFdWArc_nE3TdKWQg\/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:355px;height:auto\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:heading -->\n<h2 class=\"wp-block-heading\">Course Schedule<br><a href=\"https:\/\/drive.google.com\/file\/d\/1A9sAQdsDmyDm9nx3G7N9ZQEJW9CKE9Uf\/view?usp=drive_link\"><\/a><\/h2>\n<!-- \/wp:heading -->\n\n<!-- wp:image {\"lightbox\":{\"enabled\":false},\"id\":1471,\"width\":\"344px\",\"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\/1r-RhyerqIKhD8OiP9Du36V49t8MW_oBz\/view?usp=drive_link\"><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:344px;height:auto\"\/><\/a><\/figure>\n<!-- \/wp:image -->\n\n<!-- wp:paragraph -->\n<p><\/p>\n<!-- \/wp:paragraph -->","_et_gb_content_width":"1080","footnotes":""},"categories":[24,22],"tags":[],"class_list":["post-1318","post","type-post","status-publish","format-standard","hentry","category-compulsory-en","category-pec-track"],"_links":{"self":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1318","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=1318"}],"version-history":[{"count":7,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1318\/revisions"}],"predecessor-version":[{"id":2368,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/posts\/1318\/revisions\/2368"}],"wp:attachment":[{"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/media?parent=1318"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/categories?post=1318"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.ift.uam-csic.es\/master\/wp-json\/wp\/v2\/tags?post=1318"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}