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 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" $|\alpha |<\sqrt{8\pi }$ of the charge parameter $\alpha$. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.

arXiv commentReferences are corrected

References in corpus (6)

• A theory of regularity structures
• The dynamical sine-Gordon model
• The reconstruction theorem in Besov spaces
• The dynamical sine-Gordon model in the full subcritical regime
• Stochastic quantization associated with the $\exp (\Phi {)}_2$-quantum field model driven by space-time white noise on the torus
• Stochastic quantization of Liouville conformal field theory

Cited by in corpus (1)

• Construction of a non-Gaussian and rotation-invariant ${\Phi }^4$-measure and associated flow on ${\mathbb{R}}^3$ through stochastic quantization