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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2511.04509 |
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| _version_ | 1866918447924903936 |
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| author | Kopper, Christoph Wang, Pierre |
| author_facet | Kopper, Christoph Wang, Pierre |
| contents | We have constructed the mean-field trivial solution of the $φ^4$ theory $O(N)$ model in four dimensions in two previous papers using the flow equations of the renormalization group. Here we establish a relation between the trivial solutions we constructed and perturbation theory. We show that if an UV-cutoff is maintained, we can define a renormalized coupling constant $g$ and obtain the perturbative solutions of the mean-field flow equations at each order in perturbation theory. We prove the local Borel-summability of the renormalized mean-field perturbation theory in the presence of an UV cutoff and show that it is asymptotic to the non-perturbative solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04509 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Triviality vs perturbation theory: an analysis for mean-field $φ^4$-theory in four dimensions Kopper, Christoph Wang, Pierre Mathematical Physics We have constructed the mean-field trivial solution of the $φ^4$ theory $O(N)$ model in four dimensions in two previous papers using the flow equations of the renormalization group. Here we establish a relation between the trivial solutions we constructed and perturbation theory. We show that if an UV-cutoff is maintained, we can define a renormalized coupling constant $g$ and obtain the perturbative solutions of the mean-field flow equations at each order in perturbation theory. We prove the local Borel-summability of the renormalized mean-field perturbation theory in the presence of an UV cutoff and show that it is asymptotic to the non-perturbative solution. |
| title | Triviality vs perturbation theory: an analysis for mean-field $φ^4$-theory in four dimensions |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2511.04509 |