Instantons in $ϕ^4$ Theories: Transseries, Virial Theorems and Numerical Aspects
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| author | Giorgini, Ludovico T. Jentschura, Ulrich D. Malatesta, Enrico M. Rizzo, Tommaso Zinn-Justin, Jean |
| author_facet | Giorgini, Ludovico T. Jentschura, Ulrich D. Malatesta, Enrico M. Rizzo, Tommaso Zinn-Justin, Jean |
| contents | We discuss numerical aspects of instantons in two- and three-dimensional $ϕ^4$ theories with an internal $O(N)$ symmetry group, the so-called $N$-vector model. Combining asymptotic transseries expansions for large argument with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties are necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in $ϕ^4$ theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18191 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Instantons in $ϕ^4$ Theories: Transseries, Virial Theorems and Numerical Aspects Giorgini, Ludovico T. Jentschura, Ulrich D. Malatesta, Enrico M. Rizzo, Tommaso Zinn-Justin, Jean High Energy Physics - Theory We discuss numerical aspects of instantons in two- and three-dimensional $ϕ^4$ theories with an internal $O(N)$ symmetry group, the so-called $N$-vector model. Combining asymptotic transseries expansions for large argument with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties are necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in $ϕ^4$ theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations. |
| title | Instantons in $ϕ^4$ Theories: Transseries, Virial Theorems and Numerical Aspects |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2405.18191 |