Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2407.01309 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929732583424000 |
|---|---|
| author | Wang, Pierre Kopper, Christoph |
| author_facet | Wang, Pierre Kopper, Christoph |
| contents | The differential equations of the Wilson renormalization group are a powerful tool to study the Schwinger functions of Euclidean quantum field theory. In particular renormalization theory can be based entirely on inductively bounding their perturbatively expanded solutions. Recently the solutions of these equations for scalar field theory have been analysed rigorously without recourse to perturbation theory, at the cost of restricting to the mean-field approximation. In particular it was shown there that one-component $φ^4_4$-theory is trivial if the bare coupling constant of the UV regularized theory is not large. This paper presents progress w.r.t. Kopper's previous paper on asymptotically free solutions of the mean-field scalar flow equations: 1. The upper bound on the bare coupling is sent to infinity and the proof is extended to $O(N)$ vector models. 2. The unphysical infrared cutoff used for technical simplicity is replaced by a physical mass. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01309 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triviality proof for mean-field $φ_4^4$-theories Wang, Pierre Kopper, Christoph Mathematical Physics The differential equations of the Wilson renormalization group are a powerful tool to study the Schwinger functions of Euclidean quantum field theory. In particular renormalization theory can be based entirely on inductively bounding their perturbatively expanded solutions. Recently the solutions of these equations for scalar field theory have been analysed rigorously without recourse to perturbation theory, at the cost of restricting to the mean-field approximation. In particular it was shown there that one-component $φ^4_4$-theory is trivial if the bare coupling constant of the UV regularized theory is not large. This paper presents progress w.r.t. Kopper's previous paper on asymptotically free solutions of the mean-field scalar flow equations: 1. The upper bound on the bare coupling is sent to infinity and the proof is extended to $O(N)$ vector models. 2. The unphysical infrared cutoff used for technical simplicity is replaced by a physical mass. |
| title | Triviality proof for mean-field $φ_4^4$-theories |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2407.01309 |