$Φ^4_3$ measures on compact Riemannian $3$-manifolds
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915595618877440 |
|---|---|
| author | Bailleul, I. Dang, N. V. Ferdinand, L. Tô, T. D. |
| author_facet | Bailleul, I. Dang, N. V. Ferdinand, L. Tô, T. D. |
| contents | We construct the $Φ^4_3$ measure on an arbitrary 3-dimensional compact Riemannian manifold without boundary as an invariant probability measure of a singular stochastic partial differential equation. Proving the nontriviality and the covariance under Riemannian isometries of that measure gives a non-perturbative, non-topological interacting Euclidean quantum field theory on curved spaces in dimension 3. To control analytically several Feynman diagrams appearing in the construction of a number of random fields, we introduce a novel approach of renormalisation using microlocal and harmonic analysis. This allows to obtain a renormalized equation which involves some universal constants independent of the manifold. In a companion paper, we develop in a self-contained way all the tools from paradifferential and microlocal analysis that we use to build in our manifold setting a number of analytic and probabilistic objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_10185 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $Φ^4_3$ measures on compact Riemannian $3$-manifolds Bailleul, I. Dang, N. V. Ferdinand, L. Tô, T. D. Mathematical Physics Analysis of PDEs Classical Analysis and ODEs Probability We construct the $Φ^4_3$ measure on an arbitrary 3-dimensional compact Riemannian manifold without boundary as an invariant probability measure of a singular stochastic partial differential equation. Proving the nontriviality and the covariance under Riemannian isometries of that measure gives a non-perturbative, non-topological interacting Euclidean quantum field theory on curved spaces in dimension 3. To control analytically several Feynman diagrams appearing in the construction of a number of random fields, we introduce a novel approach of renormalisation using microlocal and harmonic analysis. This allows to obtain a renormalized equation which involves some universal constants independent of the manifold. In a companion paper, we develop in a self-contained way all the tools from paradifferential and microlocal analysis that we use to build in our manifold setting a number of analytic and probabilistic objects. |
| title | $Φ^4_3$ measures on compact Riemannian $3$-manifolds |
| topic | Mathematical Physics Analysis of PDEs Classical Analysis and ODEs Probability |
| url | https://arxiv.org/abs/2304.10185 |