Stochastic quantization associated with the $\exp (\Phi {)}_2$-quantum field model driven by space-time white noise on the torus

Abstract

We consider a quantum field model with exponential interactions on the two-dimensional torus, which is called the $\exp (\Phi {)}_2$-quantum field model or Høegh-Krohn's model. In the present paper, we study the stochastic quantization of this model by singular stochastic partial differential equations, which is recently developed. By the method, we construct a unique time-global solution and the invariant probability measure of the corresponding stochastic quantization equation, and identify with an infinite-dimensional diffusion process, which has been constructed by the Dirichlet form approach.

To appear in Journal of Evolution Equations

References in corpus (4)

• Global solutions to elliptic and parabolic ${\Phi }^4$ models in Euclidean space
• The invariant measure and the flow associated to the ${\Phi }_3^4$-quantum field model
• Elliptic stochastic quantization
• Stochastic Ricci Flow on Compact Surfaces

Cited by in corpus (5)

• Stochastic quantization of Liouville conformal field theory
• On the variational method for Euclidean quantum fields in infinite volume
• Construction of a non-Gaussian and rotation-invariant ${\Phi }^4$-measure and associated flow on ${\mathbb{R}}^3$ through stochastic quantization
• 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
• Characterization of the support for Wick powers of the additive stochastic heat equation