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$\Phi^4_3$ measures on compact Riemannian $3$-manifolds

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  • معلومة اضافية
    • Contributors:
      Laboratoire de mathématiques de Brest (LM); Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM); Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS); Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)); Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS); Institut universitaire de France (IUF); Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.); Laboratoire de Physique des 2 Infinis Irène Joliot-Curie (IJCLab); Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
    • بيانات النشر:
      HAL CCSD
    • الموضوع:
      2023
    • Collection:
      HAL-IN2P3 (Institut national de physique nucléaire et de physique des particules)
    • نبذة مختصرة :
      International audience ; We construct the $\phi^4_3$ 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 non-triviality and the local covariance under Riemannian isometries of that measure gives for the first time a non-perturbative, non-topological interacting Euclidean quantum field theory on curved spaces in dimension $3$. This answers a longstanding open problem of constructive quantum field theory on curved backgrounds. To control analytically several Feynman diagrams appearing in the construction of a number of random fields, we introduce a novel approach of renormalization 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.
    • Relation:
      info:eu-repo/semantics/altIdentifier/arxiv/2304.10185; hal-04092966; https://hal.science/hal-04092966; https://hal.science/hal-04092966/document; https://hal.science/hal-04092966/file/2304.10185.pdf; ARXIV: 2304.10185; INSPIRE: 2653033
    • Rights:
      info:eu-repo/semantics/OpenAccess
    • الرقم المعرف:
      edsbas.E9EAE91F