{"arxiv_id":"hep-th/0509135","title":"Anatomy of a gauge theory","abstract":"We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson--Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis we exhibit an intimate relation between the Slavnov-Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams.","primary_cat":"hep-th","cross_cats":["math.QA"],"submitted_at":"2005-09-17T20:20:58+00:00","latest_version":3,"source":"arxiv","source_label":"arXiv","source_url":null,"has_pdf":true,"has_source":false,"verdict":"CONDITIONAL","confidence":"MODERATE","one_line_summary":"The equality of renormalized gauge couplings (Slavnov-Taylor) is claimed to be equivalent to the existence of a loop-graded Hopf sub-algebra on the sum of all graphs at fixed loop order.","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","upvotes":0,"downvotes":0,"pith_score":0,"inbound_count":1,"_links":{"html":"https://pith.science/paper/hep-th/0509135","verdict":"/api/v1/verdicts/hep-th/0509135"}}