Construction of a Non-Gaussian and Rotation-Invariant $\Phi ^4$-Measure and Associated Flow on $\mathbb {R}^3$ Through Stochastic Quantization

Sergio Albeverio, University of Bonn, Germany, and Seiichiro Kusuoka, Kyoto University, Japan

• Chapters1. Introduction2. Weighted Besov spaces, paraproducts and estimates of functions3. Infinite-dimensional Ornstein-Uhlenbeck process4. Approximation equations and their transformation5. Bounds for the behaviour of $X^{M,N,(2)}$ in $N$6. Tightness of the laws of $\{ X^{M,N}\}$7. Properties of the constructed $\Phi ^4_3$-measureA. A sufficient condition for integrability