Global harmonic analysis for Φ⁴₃ on closed Riemannian manifolds

2023/06/13 by Bailleul, I., Dang, N. V., Ferdinand, L. +1
#35R60 #81T20 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2306.07757

Abstract

Following Parisi & Wu's paradigm of stochastic quantization, we constructed in \citeBDFT a Φ⁴ 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 \citeBDFT. In particular, we extend the approach of Jagannath--Perkowski to the vectorial Φ⁴₃ model by introducing a new Cole-Hopf transform involving random bundle maps.

Related

• Φ⁴₃ measures on compact Riemannian 3-manifolds
• A PDE construction of the Euclidean Φ⁴₃ quantum field theory
• Large Deviations of the Φ⁴₃ Measure via Stochastic Quantisation
• Interacting Quantum Fields in Curved Space: Renormalizability of φ⁴
• Regularity structures and the dynamical Φ⁴₃ model