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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2306.05305 |
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| _version_ | 1866911788940918784 |
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| author | Chandra, Ajay Ferdinand, Léonard |
| author_facet | Chandra, Ajay Ferdinand, Léonard |
| contents | We present two different arguments using stochastic analysis to construct super-renormalizable tensor field theories, namely the $\mathrm{T}^4_3$ and $\mathrm{T}^4_4$ models. The first approach is the construction of a Langevin dynamic combined with a PDE energy estimate while the second is an application of the variational approach of Barashkov and Gubinelli. By leveraging the melonic structure of divergences, regularising properties of non-local products, and controlling certain random operators, we demonstrate that for tensor field theories these arguments can be significantly simplified in comparison to what is required for $Φ^4_d$ models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_05305 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Stochastic Analysis Approach to Tensor Field Theories Chandra, Ajay Ferdinand, Léonard Probability Mathematical Physics We present two different arguments using stochastic analysis to construct super-renormalizable tensor field theories, namely the $\mathrm{T}^4_3$ and $\mathrm{T}^4_4$ models. The first approach is the construction of a Langevin dynamic combined with a PDE energy estimate while the second is an application of the variational approach of Barashkov and Gubinelli. By leveraging the melonic structure of divergences, regularising properties of non-local products, and controlling certain random operators, we demonstrate that for tensor field theories these arguments can be significantly simplified in comparison to what is required for $Φ^4_d$ models. |
| title | A Stochastic Analysis Approach to Tensor Field Theories |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2306.05305 |