Global harmonic analysis for $Φ^4_3$ on closed Riemannian manifolds
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914923026579456 |
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| author | Bailleul, I. Dang, N. V. Ferdinand, L. Tô, T. D. |
| author_facet | Bailleul, I. Dang, N. V. Ferdinand, L. Tô, T. D. |
| contents | Following Parisi \& Wu's paradigm of stochastic quantization, we constructed in \cite{BDFT} a $Φ^4$ measure on an arbitrary closed, compact Riemannian manifold of dimension $3$ as an invariant measure of a singular stochastic partial differential equation. This solves a longstanding open problem in quantum fields on curved backgrounds. In the present work, we build all the harmonic and microlocal analysis tools that are needed in \cite{BDFT}. In particular, we extend the approach of Jagannath--Perkowski to the vectorial $Φ^4_3$ model by introducing a new Cole-Hopf transform involving random bundle maps. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_07757 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global harmonic analysis for $Φ^4_3$ on closed Riemannian manifolds Bailleul, I. Dang, N. V. Ferdinand, L. Tô, T. D. Analysis of PDEs Mathematical Physics Probability 81T20, 35R60 Following Parisi \& Wu's paradigm of stochastic quantization, we constructed in \cite{BDFT} a $Φ^4$ measure on an arbitrary closed, compact Riemannian manifold of dimension $3$ as an invariant measure of a singular stochastic partial differential equation. This solves a longstanding open problem in quantum fields on curved backgrounds. In the present work, we build all the harmonic and microlocal analysis tools that are needed in \cite{BDFT}. In particular, we extend the approach of Jagannath--Perkowski to the vectorial $Φ^4_3$ model by introducing a new Cole-Hopf transform involving random bundle maps. |
| title | Global harmonic analysis for $Φ^4_3$ on closed Riemannian manifolds |
| topic | Analysis of PDEs Mathematical Physics Probability 81T20, 35R60 |
| url | https://arxiv.org/abs/2306.07757 |