Stochastic quantization associated with the $\exp(Φ)_2$-quantum field model driven by space-time white noise on the torus
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866909599925272576 |
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| author | Hoshino, Masato Kawabi, Hiroshi Kusuoka, Seiichiro |
| author_facet | Hoshino, Masato Kawabi, Hiroshi Kusuoka, Seiichiro |
| contents | We consider a quantum field model with exponential interactions on the two-dimensional torus, which is called the $\exp (Φ)_{2}$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1907_07921 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Stochastic quantization associated with the $\exp(Φ)_2$-quantum field model driven by space-time white noise on the torus Hoshino, Masato Kawabi, Hiroshi Kusuoka, Seiichiro Probability Mathematical Physics Analysis of PDEs We consider a quantum field model with exponential interactions on the two-dimensional torus, which is called the $\exp (Φ)_{2}$-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. |
| title | Stochastic quantization associated with the $\exp(Φ)_2$-quantum field model driven by space-time white noise on the torus |
| topic | Probability Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/1907.07921 |