[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-656821-105":59,"doc-detail-656821-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","physics-424-lecture-16-the-feynman-rules-for-qed","Physics 424 Lecture 16 - The Feynman Rules for QED","","Physics 424 Lecture 16 presents a structured recipe for constructing QED amplitudes from Feynman diagrams. It outlines three steps: draw the diagram with the minimum number of vertices, label each line’s four-momentum while enforcing four-momentum conservation at every vertex, and build the amplitude from vertex factors, propagators for internal lines, and wavefunctions for external lines. The lecture further clarifies photon and fermion propagator structure, gauge conditions such as Coulomb gauge and related Lorentz condition properties, and explains why external line factors must be placed outside to yield a scalar amplitude.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/physics-424-lecture-16-the-feynman-rules-for-qed/656821/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/physics-424-lecture-16-the-feynman-rules-for-qed/656821.png","ImageObject",300,407,{"name":92,"@type":93},"Ezra","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-25",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the purpose of the Feynman rules for QED in this lecture?","Question",{"text":112,"@type":113},"They provide a recipe for constructing an amplitude from a Feynman diagram by turning diagram elements into algebraic factors.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What are the three steps to build a QED amplitude from a diagram?",{"text":117,"@type":113},"Draw the diagram with the minimum number of vertices, label four-momenta with conservation at each vertex, then combine vertex factors, internal propagators, and external wavefunctions.",{"name":119,"@type":110,"acceptedAnswer":120},"Why must external line factors be placed on the outside?",{"text":121,"@type":113},"Because the vertex factors and fermion propagators involve matrices, while the final amplitude must be a scalar, requiring external factors to sit outside the matrix products.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},656821,1792971092,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},1099514068035,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Feynman rules for QED  \nThe Feynman Rules for QED Setting up Amplitudes Casimir's Trick  \nTrace Theorems  \nSlides from Sobie and Blokland  \n􀀀 􀀀 􀀀 􀀀  \nPhysics 424 Lecture 16 Page 1  \n\n| Electrons and positrons |\n| --- |\n| spinors\u003Cbr>and (s = spin) satisfy the Dirac equations and\u003Cbr>adjoints\u003Cbr> and  satisfy  and \u003Cbr>orthogonality\u003Cbr> and \u003Cbr>normalization\u003Cbr>and \u003Cbr>completeness\u003Cbr> and\u003Cbr>✁\u003Cbr>☛\u003Cbr>☞\u003Cbr>✝\u003Cbr>☎ ☛\u003Cbr>✄ ✠\u003Cbr>✂ ✟\u003Cbr>✝ ✞☎ ✏\u003Cbr>✄ ✎\u003Cbr>✞\u003Cbr>✓\u003Cbr>✑\u003Cbr>✒\u003Cbr>✒\u003Cbr>✑\u003Cbr>✂\u003Cbr>✏\u003Cbr>✎\u003Cbr>✍\u003Cbr>☛\u003Cbr>☞\u003Cbr>☛\u003Cbr>✟✠\u003Cbr>✁\u003Cbr>✕\u003Cbr>✠\u003Cbr>✔\u003Cbr>✂\u003Cbr>✑\u003Cbr>✂\u003Cbr>✕\u003Cbr>✠\u003Cbr>✔✞\u003Cbr>✑\u003Cbr>✞\u003Cbr>✍\u003Cbr>☛\u003Cbr>☞\u003Cbr>☛\u003Cbr>✠\u003Cbr>✟\u003Cbr>✂\u003Cbr>✏\u003Cbr>✎\u003Cbr>✑\u003Cbr>✒\u003Cbr>☛\u003Cbr>☞\u003Cbr>☛\u003Cbr>✠\u003Cbr>✟\u003Cbr>✞\u003Cbr>✏\u003Cbr>✎\u003Cbr>✓\u003Cbr>✑\u003Cbr>✒\u003Cbr>✁\u003Cbr>✒\u003Cbr>✑\u003Cbr>✝\u003Cbr>✗\u003Cbr>✄\u003Cbr>✂\u003Cbr>✝\u003Cbr>✖\u003Cbr>✄\u003Cbr>✂\u003Cbr>✒\u003Cbr>✑\u003Cbr>✝\u003Cbr>✗\u003Cbr>✄\u003Cbr>✞\u003Cbr>✝\u003Cbr>✖\u003Cbr>✄\u003Cbr>✞\u003Cbr>✎\u003Cbr>✘\u003Cbr>✍\u003Cbr>✑\u003Cbr>✞\u003Cbr>✞\u003Cbr>✎\u003Cbr>✘\u003Cbr>✑\u003Cbr>✂\u003Cbr>✂\u003Cbr>✁\u003Cbr>✎\u003Cbr>✓\u003Cbr>☛\u003Cbr>☞\u003Cbr>☛\u003Cbr>✠\u003Cbr>✑\u003Cbr>✝☎✄\u003Cbr>✂\u003Cbr>✝☎✄\u003Cbr>✂\u003Cbr>☎\u003Cbr>✙\u003Cbr>✁\u003Cbr>✎\u003Cbr>✍\u003Cbr>☛\u003Cbr>☞\u003Cbr>☛\u003Cbr>✠\u003Cbr>✑\u003Cbr>✝☎✄\u003Cbr>✞\u003Cbr>✝☎✄\u003Cbr>✞\u003Cbr>☎\u003Cbr>✙ |\n\nPhysics 424 Lecture 16 Page 2  \nPhotons  \n✏  \n☞  \n✟  \n☛  \n%  \n$  \n\\#  \n!  \n✤  \n✣  \n✢  \n✑  \n✏  \n✜  \n✟  \n☛  \n✛  \nLorentz condition orthogonality normalization  \nCoulomb gauge  \nand  \nCompleteness  \n✗  \n☞  \n-  \n✏  \n*  \n☞  \n☞  \n✟  \n✍  \n*  \n,  \n✒  \n✑  \n✑  \n*  \n) ✏  \n✝  \n( ☎  \n✒ & ✄  \n% %  \n✑ ✬ ✟  \n✒ ✏  \n✑ ✝✗✄ ✑ ✒ ✝☎✄  \n☛ ☛ %  \n☞  \n☛ & %✝ &% ✑ ✟☎☛ ☛ ✄✖% ☛% ✕% ✙  \n%  \n✁ ✁ ✁ ✁ ✁  \nPhysics 424 Lecture 16 Page 3  \nThe Feynman Rules for QED  \nThe Feynman rules provide the recipe for constructing an amplitude from a Feynman diagram.  \nStep 1: For a particular process of interest, draw a Feynman diagram with the minimum number of vertices. There maybe more than one.  \n.  \n✁  \n4  \n☞  \n/  \n1 ✣  \n3  \n☞  \n/  \n✤  \n✣  \n✠  \n✗  \n☞  \n/  \n1 ✣  \n✖  \n☞  \n/  \n✤  \n✣  \nPhysics 424 Lecture 16 Page 4  \nThe Feynman Rules for QED  \nStep 2: For each Feynman diagram, label the four-momentum of each line, enforcing four-momentum conservation at every vertex. Note that arrows are only present on fermion lines and they represent particle 􀀃ow, not momentum.  \n4 ☞  \n/  \n1 ✣  \n3  \n☞  \n/  \n✤  \n✣  \n✁  \n✠  \n✗  \n☞  \n/  \n1 ✣  \n✖  \n☞  \n/  \n✤  \n✣  \nPhysics 424 Lecture 16 Page 5  \nStep 3: The amplitude depends on  \n1. Vertex factors  \n2. Propagators for internal lines  \n3. Wavefunctions for external lines  \n􀀀  \nPhysics 424 Lecture 16 Page 6  \nVertex Factors  \nEvery QED vertex,  \ncontributes a factor of  \n.  \nis a dimensionless coupling constant and is related to the  \n􀀂ne-structure constant by   \n􀀀  \n5 5  \n6  \n\u003C  \n6  \n78:  \n>=  \n:  \n8  \n􀀀  \nPhysics 424 Lecture 16 Page 7  \n\n| Propagators |\n| --- |\n| Each internal photon connects two vertices of the form and , so we should expect the photon propagator to contract the indices and .\u003Cbr>Photon propagator: \u003Cbr>Internal fermions have a more complicated propagator,\u003Cbr>/\u003Cbr>Fermion propagator: \u003Cbr>The sign of matters here 􀂗 we take it to be in the same direction as the fermion arrow.\u003Cbr>C\u003Cbr>B 6\u003Cbr>:\u003Cbr>78\u003Cbr>􀀀\u003Cbr>D\u003Cbr>\u003C\u003Cbr>6\u003Cbr>:\u003Cbr>78\u003Cbr>B\u003Cbr>\u003C\u003Cbr>8 ?\u003Cbr>7 FE\u003Cbr>K ?\u003Cbr>HI IE\u003Cbr>F ?\u003Cbr>G7 F\u003Cbr>F\u003Cbr>􀀀 |\n\nPhysics 424 Lecture 16 Page 8  \nExternal Lines  \nSince both the vertex factor and the fermion propagators involve matrices, but the amplitude must be a scalar, the external line factors must sit on the outside.  \nWork backwards along every fermion line using:  \n@  \nL  \n@  \n􀀀  \n􀀀  \n\n| | | | | | |\n| --- | --- | --- | --- | --- | --- |\n\n\n| in\u003Cbr>M 5 | out\u003Cbr>M 5 | in\u003Cbr>N 5 | out\u003Cbr>N 5 | in\u003Cbr>6 | out\u003Cbr>6 |\n| --- | --- | --- | --- | --- | --- |\n| O | PO | PQ | Q | \u003C S | T \u003C\u003Cbr>S |\n\nPhysics 424 Lecture 16 Page 9  \n\n| Matrix elements I\u003Cbr>follow fermion lines backward to give \u003Cbr>K\u003Cbr>V\u003Cbr>GO\u003Cbr>\u003C 6\u003Cbr>78\u003Cbr>K\u003Cbr>U\u003Cbr>GO\u003Cbr>5 |  |\n| --- | --- |\n| | 6 |\n| 5 |  |\n\nPhysics 424 Lecture 16 Page 10","cbCairiga1aY8wdW","https://ap.wps.com/l/cbCairiga1aY8wdW","pdf",149247,31,"English","# The Feynman Rules for QED\n## Constructing amplitudes from diagrams\n## Vertex factors, propagators, and external line factors\n## Photon and fermion propagators","[{\"question\":\"What is the purpose of the Feynman rules for QED in this lecture?\",\"answer\":\"They provide a recipe for constructing an amplitude from a Feynman diagram by turning diagram elements into algebraic factors.\"},{\"question\":\"What are the three steps to build a QED amplitude from a diagram?\",\"answer\":\"Draw the diagram with the minimum number of vertices, label four-momenta with conservation at each vertex, then combine vertex factors, internal propagators, and external wavefunctions.\"},{\"question\":\"Why must external line factors be placed on the outside?\",\"answer\":\"Because the vertex factors and fermion propagators involve matrices, while the final amplitude must be a scalar, requiring external factors to sit outside the matrix products.\"}]","Physics 424 Lecture 16 - The Feynman Rules for QED | PDF",78]