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Phys. A: Math. Theor."],"published-print":{"date-parts":[[2025,8,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We study the path integral quantization of the topological 3<jats:italic>BF<\/jats:italic> theory, whose gauge symmetry is described by a 3-group. This theory is relevant for the quantization of general relativity coupled to Standard Model of elementary particles. We explicitly construct a state sum corresponding to the discretized path integral of a 3<jats:italic>BF<\/jats:italic> action. Being a topological invariant of 4-dimensional manifolds with boundary, this state sum gives rise to a topological quantum field theory (TQFT), realized as a functor between the category of cobordisms and the category of Hilbert spaces. After an introduction to appropriate category theory concepts and the construction of the state sum, we provide an explicit proof that it satisfies all Atiyah\u2019s axioms, and thus represents a genuine TQFT. The formulation of this TQFT represents a major step in the spinfoam quantization programme for a realistic theory of quantum gravity with matter.<\/jats:p>","DOI":"10.1088\/1751-8121\/adfb14","type":"journal-article","created":{"date-parts":[[2025,8,13]],"date-time":"2025-08-13T22:51:52Z","timestamp":1755125512000},"page":"345203","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["The 3BF theory as a TQFT"],"prefix":"10.1088","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2310-5281","authenticated-orcid":true,"given":"T","family":"Radenkovi\u0107","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6977-4870","authenticated-orcid":true,"given":"M","family":"Vojinovi\u0107","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2025,8,26]]},"reference":[{"year":"2006","author":"Becker","key":"aadfb14bib1"},{"year":"2004","author":"Zwiebach","key":"aadfb14bib2"},{"year":"1998","author":"Polchinski","key":"aadfb14bib3"},{"key":"aadfb14bib4","doi-asserted-by":"publisher","first-page":"2244","DOI":"10.1103\/PhysRevLett.57.2244","article-title":"New variables for classical and quantum gravity","volume":"57","author":"Ashtekar","year":"1986","journal-title":"Phys. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2025-04-09","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-08-13","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-08-26","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}