Dirac traces and the Tutte polynomial
Abstract Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the consequence of replacing 4-dimensional Dirac m...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)235 |
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| _version_ | 1849470062758461440 |
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| author | Joshua Lin |
| author_facet | Joshua Lin |
| author_sort | Joshua Lin |
| collection | DOAJ |
| description | Abstract Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the consequence of replacing 4-dimensional Dirac matrices with d-dimensional counterparts for arbitrary complex values of d. In this work, a connection between traces of d-dimensional Dirac matrices and computations of the Tutte polynomial of associated graphs is proven. The time complexity of computing Dirac traces is analysed by this connection, and improvements to algorithms for computing Dirac traces are proposed. |
| format | Article |
| id | doaj-art-0be590921de4400aac81e7497524c612 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-0be590921de4400aac81e7497524c6122025-08-20T03:25:16ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025512610.1007/JHEP05(2025)235Dirac traces and the Tutte polynomialJoshua Lin0Center for Theoretical Physics, Massachusetts Institute of TechnologyAbstract Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the consequence of replacing 4-dimensional Dirac matrices with d-dimensional counterparts for arbitrary complex values of d. In this work, a connection between traces of d-dimensional Dirac matrices and computations of the Tutte polynomial of associated graphs is proven. The time complexity of computing Dirac traces is analysed by this connection, and improvements to algorithms for computing Dirac traces are proposed.https://doi.org/10.1007/JHEP05(2025)235Renormalization and RegularizationScattering Amplitudes |
| spellingShingle | Joshua Lin Dirac traces and the Tutte polynomial Journal of High Energy Physics Renormalization and Regularization Scattering Amplitudes |
| title | Dirac traces and the Tutte polynomial |
| title_full | Dirac traces and the Tutte polynomial |
| title_fullStr | Dirac traces and the Tutte polynomial |
| title_full_unstemmed | Dirac traces and the Tutte polynomial |
| title_short | Dirac traces and the Tutte polynomial |
| title_sort | dirac traces and the tutte polynomial |
| topic | Renormalization and Regularization Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP05(2025)235 |
| work_keys_str_mv | AT joshualin diractracesandthetuttepolynomial |