Global harmonic analysis for ${\Phi }_3^4$ on closed Riemannian manifolds

Abstract

Following Parisi \& Wu's paradigm of stochastic quantization, we constructed in \cite{BDFT} a ${\Phi }^4$ 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 ${\Phi }_3^4$ model by introducing a new Cole-Hopf transform involving random bundle maps.

Last version, to appear in The Journal of Geometric Analysis

Cited by in corpus (1)

• The Tensor Track VIII: Stochastic Analysis