Resummation in QFT with Meijer G-functions
We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using this technique, we consider in detail the ϕ4 model where we est...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2019-04-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321319300422 |
| _version_ | 1811329840374087680 |
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| author | Oleg Antipin Alessio Maiezza Juan Carlos Vasquez |
| author_facet | Oleg Antipin Alessio Maiezza Juan Carlos Vasquez |
| author_sort | Oleg Antipin |
| collection | DOAJ |
| description | We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using this technique, we consider in detail the ϕ4 model where we estimate the non-perturbative β-function and prove that its asymptotic behavior correctly reproduces instantonic effects calculated using semiclassical methods. After reviewing the emergence of the renormalons in this theory, we also speculate on how one can resum them. Finally, we resum the non-perturbative β-function of abelian and non-abelian gauge-fermion theories and analyze the behavior of these theories as a function of the number of fermion flavors. While in the former no fixed points are found, in the latter, a richer phase diagram is uncovered and illustrated by the regions of confinement, large-distance conformality, and asymptotic safety. |
| first_indexed | 2024-04-13T15:51:02Z |
| format | Article |
| id | doaj.art-8320b65e6e9b4cd2b1f66907291bb222 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-04-13T15:51:02Z |
| publishDate | 2019-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-8320b65e6e9b4cd2b1f66907291bb2222022-12-22T02:40:51ZengElsevierNuclear Physics B0550-32132019-04-019417290Resummation in QFT with Meijer G-functionsOleg Antipin0Alessio Maiezza1Juan Carlos Vasquez2Ruder Bošković Institute, Division of Theoretical Physics, Bijenička cesta 54, 10000, Zagreb, CroatiaRuder Bošković Institute, Division of Theoretical Physics, Bijenička cesta 54, 10000, Zagreb, CroatiaUniversidad Técnica Federico Santa María & CCTVAL, Valparaíso, Chile; Corresponding author.We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using this technique, we consider in detail the ϕ4 model where we estimate the non-perturbative β-function and prove that its asymptotic behavior correctly reproduces instantonic effects calculated using semiclassical methods. After reviewing the emergence of the renormalons in this theory, we also speculate on how one can resum them. Finally, we resum the non-perturbative β-function of abelian and non-abelian gauge-fermion theories and analyze the behavior of these theories as a function of the number of fermion flavors. While in the former no fixed points are found, in the latter, a richer phase diagram is uncovered and illustrated by the regions of confinement, large-distance conformality, and asymptotic safety.http://www.sciencedirect.com/science/article/pii/S0550321319300422 |
| spellingShingle | Oleg Antipin Alessio Maiezza Juan Carlos Vasquez Resummation in QFT with Meijer G-functions Nuclear Physics B |
| title | Resummation in QFT with Meijer G-functions |
| title_full | Resummation in QFT with Meijer G-functions |
| title_fullStr | Resummation in QFT with Meijer G-functions |
| title_full_unstemmed | Resummation in QFT with Meijer G-functions |
| title_short | Resummation in QFT with Meijer G-functions |
| title_sort | resummation in qft with meijer g functions |
| url | http://www.sciencedirect.com/science/article/pii/S0550321319300422 |
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