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

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

Chapters 1. Introduction 2. Weighted Besov spaces, paraproducts and estimates of functions 3. Infinite-dimensional Ornstein-Uhlenbeck process 4. Approximation equations and their transformation 5. 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 $\Phi ^4_3$-measure A. A sufficient condition for integrability