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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Main Author: Joshua Lin
Format: Article
Language:English
Published: SpringerOpen 2025-05-01
Series:Journal of High Energy Physics
Subjects:
Online Access:https://doi.org/10.1007/JHEP05(2025)235
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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
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institution Kabale University
issn 1029-8479
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publishDate 2025-05-01
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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