{"product_id":"hopf-algebras-and-quantum-field-theory-von-angela-mestre","title":"Hopf algebras and quantum field theory","description":"\u003cp\u003eIn perturbative quantum field theory, the n-point functions consist, in general, of an infinity of Feynman graphs. Traditionally, these are generated via  functional methods. This book describes the relation between complete, connected, and 1-particle irreducible n-point functions   directly at the level of the Hopf algebra of time-ordered field operators. The ensembles of time-ordered n-point functions are  simply linear forms on this algebra. It is showed, for instance, that the complete and connected n-point functions are elegantly related through the convolution  product (induced by the coproduct). In this setting, a simple algebraic relation between connected and 1-particle irreducible n-point functions is  derived, while the connected n-point functions are expressed in terms of their loop order contributions.  At the center of the work stands a Hopf algebraic representation of graphs and a new algorithm to recursively generate all trees or all connected graphs and their values as Feynman graphs. This monograph presents a clear and self-contained exposition of all the results and their proofs. An introduction to the basic concepts required for the reading is also given.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783659131738\"\u003e\u003ch3\u003eCombinatorics of n-point functions via Hopf algebra\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783659131738","offer_id":39487707218013,"sku":"9783659131738","price":49.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/d44b4787-5a56-4d43-9012-6a906577afb9.jpg?v=1757394562","url":"https:\/\/shop.autorenwelt.de\/products\/hopf-algebras-and-quantum-field-theory-von-angela-mestre","provider":"Autorenwelt Shop","version":"1.0","type":"link"}