Stochastic quantization associated with the exp (Phi )_2-quantum field model driven by space-time white noise on the torus in the full L^1-regime

Abstract

The present paper is a continuation of our previous work (Hoshino et al., J Evol Equ 21:339–375, 2021) on the stochastic quantization of the exp (Phi )_2-quantum field model on the two-dimensional torus. Making use of key properties of Gaussian multiplicative chaos and refining the method for singular SPDEs introduced in the previous work, we construct a unique time-global solution to the corresponding parabolic stochastic quantization equation in the full “L^{1}-regime” vert alpha vert <sqrt{8pi } of the charge parameter alpha . We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.