Global harmonic analysis for Φ 4 3 on closed Riemannian manifolds

Following Parisi & Wu's paradigm of stochastic quantization, we constructed in [6] a Φ 4 measure on an arbitrary compact, boundaryless, Riemannian manifold as an invariant measure of a singular stochastic partial differential equation. The present work is a companion to [6]. We describe here in detail the harmonic and microlocal analysis tools that we used. We also introduce some new tools to treat the vectorial Φ 4 3 model. This relies on a new Cole-Hopf transform involving random bundle maps. We do not aim here for the greatest generality; rather, we tried to keep our exposition relatively self-contained and pedagogical enough in the hope that the techniques we show can be used in other settings