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

Masato Hoshino; Hiroshi Kawabi; Seiichiro Kusuoka

doi:10.1007/s00028-020-00583-0

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arXiv · 1907.07921

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

Masato Hoshino·Hiroshi Kawabi·Seiichiro Kusuoka

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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 H{\o}egh-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.

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BibTeX RIS

Masato Hoshino, Hiroshi Kawabi, Seiichiro Kusuoka. 2019-07-18. Stochastic quantization associated with the $\exp(\Phi)_2$-quantum field model driven by space-time white noise on the torus. https://doi.org/10.1007/s00028-020-00583-0

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