Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme
Various combinatorially non-local field theories are known to be renormalizable. Still, explicit calculations of amplitudes are very rare and restricted to matrix field theory. In this contribution, I want to demonstrate how the BPHZ momentum scheme in terms of the Connes-Kreimer Hopf algebra applie...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211433 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme. Johannes Thürigen. SIGMA 17 (2021), 094, 14 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707593675276288 |
|---|---|
| author | Thürigen, Johannes |
| author_facet | Thürigen, Johannes |
| citation_txt | Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme. Johannes Thürigen. SIGMA 17 (2021), 094, 14 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Various combinatorially non-local field theories are known to be renormalizable. Still, explicit calculations of amplitudes are very rare and restricted to matrix field theory. In this contribution, I want to demonstrate how the BPHZ momentum scheme in terms of the Connes-Kreimer Hopf algebra applies to any combinatorially non-local field theory that is renormalizable. This algebraic method improves the understanding of known results in noncommutative field theory in its matrix formulation. Furthermore, I use it to provide new explicit perturbative calculations of amplitudes in tensorial field theories of rank > 2.
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| first_indexed | 2026-03-19T04:35:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211433 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T04:35:18Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Thürigen, Johannes 2026-01-02T08:31:56Z 2021 Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme. Johannes Thürigen. SIGMA 17 (2021), 094, 14 pages 1815-0659 2020 Mathematics Subject Classification: 05C10; 16T05; 16T30; 81T15; 81T18; 81T32 arXiv:2103.01136 https://nasplib.isofts.kiev.ua/handle/123456789/211433 https://doi.org/10.3842/SIGMA.2021.094 Various combinatorially non-local field theories are known to be renormalizable. Still, explicit calculations of amplitudes are very rare and restricted to matrix field theory. In this contribution, I want to demonstrate how the BPHZ momentum scheme in terms of the Connes-Kreimer Hopf algebra applies to any combinatorially non-local field theory that is renormalizable. This algebraic method improves the understanding of known results in noncommutative field theory in its matrix formulation. Furthermore, I use it to provide new explicit perturbative calculations of amplitudes in tensorial field theories of rank > 2. I would like to thank A. Hock and R. Wulkenhaar for discussions on the forest formula in matrix field theory, as well as the referees for their very valuable comments and suggestions. I am deeply grateful to D. Kreimer for advice and support, in particular in developing the research project this work is part of, which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under the project number 418838388. Further support comes from the DFG under Germany’s Excellence Strategy EXC 2044–390685587, Mathematics Münster: Dynamics–Geometry–Structure. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme Article published earlier |
| spellingShingle | Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme Thürigen, Johannes |
| title | Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme |
| title_full | Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme |
| title_fullStr | Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme |
| title_full_unstemmed | Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme |
| title_short | Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme |
| title_sort | renormalization in combinatorially non-local field theories: the bphz momentum scheme |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211433 |
| work_keys_str_mv | AT thurigenjohannes renormalizationincombinatoriallynonlocalfieldtheoriesthebphzmomentumscheme |