A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem
Quantum Field Theory, as the keystone of particle physics, has offered great insights into deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of divergent quantities in intermediary steps of the calculatio...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/6/956 |
| _version_ | 1797532373419556864 |
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| author | Dafne Carolina Arias-Perdomo Adriano Cherchiglia Brigitte Hiller Marcos Sampaio |
| author_facet | Dafne Carolina Arias-Perdomo Adriano Cherchiglia Brigitte Hiller Marcos Sampaio |
| author_sort | Dafne Carolina Arias-Perdomo |
| collection | DOAJ |
| description | Quantum Field Theory, as the keystone of particle physics, has offered great insights into deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of divergent quantities in intermediary steps of the calculation, which encompasses the need for some regularization/renormalization prescription. As an alternative to traditional methods, based on the analytic extension of space–time dimension, frameworks that stay in the physical dimension have emerged; Implicit Regularization is one among them. We briefly review the method, aiming to illustrate how Implicit Regularization complies with the BPHZ theorem, which implies that it respects unitarity and locality to arbitrary loop order. We also pedagogically discuss how the method complies with gauge symmetry using one- and two-loop examples in QED and QCD. |
| first_indexed | 2024-03-10T10:58:13Z |
| format | Article |
| id | doaj.art-184737ab950149d7adc616f2d2f1ed9b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T10:58:13Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-184737ab950149d7adc616f2d2f1ed9b2023-11-21T21:42:10ZengMDPI AGSymmetry2073-89942021-05-0113695610.3390/sym13060956A Brief Review of Implicit Regularization and Its Connection with the BPHZ TheoremDafne Carolina Arias-Perdomo0Adriano Cherchiglia1Brigitte Hiller2Marcos Sampaio3CCNH Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André 09210-580, SP, BrazilCCNH Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André 09210-580, SP, BrazilCFisUC, Department of Physics, University of Coimbra, P-3004-516 Coimbra, PortugalCCNH Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, Santo André 09210-580, SP, BrazilQuantum Field Theory, as the keystone of particle physics, has offered great insights into deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of divergent quantities in intermediary steps of the calculation, which encompasses the need for some regularization/renormalization prescription. As an alternative to traditional methods, based on the analytic extension of space–time dimension, frameworks that stay in the physical dimension have emerged; Implicit Regularization is one among them. We briefly review the method, aiming to illustrate how Implicit Regularization complies with the BPHZ theorem, which implies that it respects unitarity and locality to arbitrary loop order. We also pedagogically discuss how the method complies with gauge symmetry using one- and two-loop examples in QED and QCD.https://www.mdpi.com/2073-8994/13/6/956renormalization/regularizationrenormalization group functionsBPHZ theorem |
| spellingShingle | Dafne Carolina Arias-Perdomo Adriano Cherchiglia Brigitte Hiller Marcos Sampaio A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem Symmetry renormalization/regularization renormalization group functions BPHZ theorem |
| title | A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem |
| title_full | A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem |
| title_fullStr | A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem |
| title_full_unstemmed | A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem |
| title_short | A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem |
| title_sort | brief review of implicit regularization and its connection with the bphz theorem |
| topic | renormalization/regularization renormalization group functions BPHZ theorem |
| url | https://www.mdpi.com/2073-8994/13/6/956 |
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