{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-galois-coaction-on-4-periods","title":"The Galois coaction on $φ^4$ periods","arxiv_id":"1603.04289","date":"2016-03-14","proceeding":null,"authors":["Erik Panzer","Oliver Schnetz"],"abstract":"We report on calculations of Feynman periods of primitive log-divergent $\\phi^4$ graphs up to eleven loops. The structure of $\\phi^4$ periods is described by a series of conjectures. In particular, we discuss the possibility that $\\phi^4$ periods are a comodule under the Galois coaction. Finally, we compare the results with the periods of primitive log-divergent non-$\\phi^4$ graphs up to eight loops and find remarkable differences to $\\phi^4$ periods. Explicit results for all periods we could compute are provided in ancillary files.","url_abs":"http://arxiv.org/abs/1603.04289v2","url_pdf":"http://arxiv.org/pdf/1603.04289v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-galois-coaction-on-4-periods","repo_url":"https://github.com/bluenote-1577/c2invariant_cw_code","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}