[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657382-105":59,"doc-detail-657382-en":124},{"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":117,"head_meta":119,"extra_data":121,"updated_unix":123},105,"en","feynman-diagrams-and-the-s-matrix-and-outer-space-summer-2020-exercise-6","Feynman Diagrams and the S-Matrix and Outer Space - Summer 2020 - Exercise 6","","This document provides a set of theoretical physics exercises related to Feynman diagrams, the S-matrix, and graph theory, authored by Dirk Kreimer for the Summer 2020 course. The content focuses on the analysis of a specific graph structure, identified as a wheel with three spokes, which involves external and internal edges labeled from e1 to e10. Students are tasked with calculating the number of spanning trees, identifying all such trees, determining normal thresholds, and evaluating reduced graphs for the given system. Furthermore, the problem requires finding a complete refinement of vertices and external edges for a chosen spanning tree, challenging students to apply advanced mathematical concepts to quantum field theory representations. This exercise serves as a critical assessment tool for understanding the complexity of perturbative quantum field theory and the combinatorial properties inherent in Feynman diagrammatic expansions, reflecting academic standards at Humboldt University in Berlin.",{"@graph":69,"@context":116},[70,84,99],{"@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":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/feynman-diagrams-and-the-s-matrix-and-outer-space-summer-2020-exercise-6/657382/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":93,"encodingFormat":92,"isAccessibleForFree":94,"interactionStatistic":95},"DigitalDocument",{"name":87,"@type":88},"Đào","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/pdf","2026-10-26",true,{"@type":96,"interactionType":97,"userInteractionCount":4},"InteractionCounter",{"@type":98},"ViewAction",{"@type":100,"mainEntity":101},"FAQPage",[102,108,112],{"name":103,"@type":104,"acceptedAnswer":105},"What is the primary subject of the exercise?","Question",{"text":106,"@type":107},"The exercise concerns Feynman diagrams, the S-matrix, and their application to a specific graph structure described as a wheel with three spokes.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"How many edges are involved in the diagram?",{"text":111,"@type":107},"The graph includes external edges labeled e1 through e4 and internal edges labeled e5 through e10.",{"name":113,"@type":104,"acceptedAnswer":114},"What are the specific tasks required for the wheel graph?",{"text":115,"@type":107},"Students must count the spanning trees, identify them all, determine normal thresholds, evaluate reduced graphs, and find a complete refinement of vertices and external edges.","https://schema.org",{"og:url":83,"og:type":118,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":120,"canonical":83},"index,follow",{"doc_id":122,"site_id":62},657382,1792978315,{"code":4,"msg":5,"data":125},{"doc_id":122,"user_id":126,"nickname":87,"user_avatar":127,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":8,"language":133,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":134,"faqs":135,"seo_title":136,"seo_description":67,"update_tm":123,"read_time":81},1374402968488,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","FEYNMAN DIAGRAMS AND THE S-MATRIX, AND OUTER SPACE  \n(SUMMER 2020)  \nDIRK KREIMER (EXERC. MAY 06, 2020)  \n1. The wheel with three spokes  \nConsider  \n\n| 2 | | 3 |\n| --- | --- | --- |\n\non external edges e 1 ; 􀀁 􀀁 􀀁 ; e4 and internal e5 ; 􀀁 􀀁 􀀁 ; e 10 .  \n􀀏 How many spanning trees?  \n􀀏 Find them all!  \n􀀏 Determine all normal thresholds!  \n􀀏 Determine the reduced graphs!  \n􀀏 Find for a chosen spanning tree a complete re􀀌nement of the vertices/external edges!  \nHumboldt U. Berlin","cbCaird9X69qom0j","https://ap.wps.com/l/cbCaird9X69qom0j","pdf",83924,"English","# Exercise Overview\n## Problem 1: The Wheel with Three Spokes\n## Required Tasks","[{\"question\":\"What is the primary subject of the exercise?\",\"answer\":\"The exercise concerns Feynman diagrams, the S-matrix, and their application to a specific graph structure described as a wheel with three spokes.\"},{\"question\":\"How many edges are involved in the diagram?\",\"answer\":\"The graph includes external edges labeled e1 through e4 and internal edges labeled e5 through e10.\"},{\"question\":\"What are the specific tasks required for the wheel graph?\",\"answer\":\"Students must count the spanning trees, identify them all, determine normal thresholds, evaluate reduced graphs, and find a complete refinement of vertices and external edges.\"}]","Feynman Diagrams and the S-Matrix and Outer Space - Summer 2020 - Exercise 6 | PDF"]