Stochastic quantization associated with the exp (Φ) 2 -quantum field model driven by space-time white noise on the torus in the full L1 -regime

Masato Hoshino; Hiroshi Kawabi; Seiichiro Kusuoka

doi:10.1007/s00440-022-01126-z

Stochastic quantization associated with the exp (Φ) ₂ -quantum field model driven by space-time white noise on the torus in the full L¹ -regime

Masato Hoshino, Hiroshi Kawabi, Seiichiro Kusuoka

Faculty of Economics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 (Φ) 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 “L¹-regime” |α|<8π of the charge parameter α. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.

Original language	English
Pages (from-to)	391-447
Number of pages	57
Journal	Probability Theory and Related Fields
Volume	185
Issue number	1-2
DOIs	https://doi.org/10.1007/s00440-022-01126-z
Publication status	Published - 2023 Feb

Keywords

Dirichlet form
Gaussian multiplicative chaos
Høegh-Krohn model
Singular SPDE
Stochastic quantization

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1007/s00440-022-01126-z

Cite this

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title = "Stochastic quantization associated with the exp (Φ) 2 -quantum field model driven by space-time white noise on the torus in the full L1 -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 (Φ) 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 “L1-regime” |α|<8π of the charge parameter α. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.",

keywords = "Dirichlet form, Gaussian multiplicative chaos, H{\o}egh-Krohn model, Singular SPDE, Stochastic quantization",

author = "Masato Hoshino and Hiroshi Kawabi and Seiichiro Kusuoka",

note = "Funding Information: The authors are grateful to Professor Makoto Nakashima for helpful discussions on Gaussian multiplicative chaos, and to Professor Ryo Takada for helpful comments on the references on Besov spaces. They also thank anonymous two referees for helpful suggestions that improved the quality of the present paper. This work was partially supported by JSPS KAKENHI Grant Numbers 17K05300, 17K14204, 19K14556, 20K03639 and 21H00988. Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2023",

month = feb,

doi = "10.1007/s00440-022-01126-z",

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AU - Hoshino, Masato

AU - Kawabi, Hiroshi

AU - Kusuoka, Seiichiro

N1 - Funding Information: The authors are grateful to Professor Makoto Nakashima for helpful discussions on Gaussian multiplicative chaos, and to Professor Ryo Takada for helpful comments on the references on Besov spaces. They also thank anonymous two referees for helpful suggestions that improved the quality of the present paper. This work was partially supported by JSPS KAKENHI Grant Numbers 17K05300, 17K14204, 19K14556, 20K03639 and 21H00988. Publisher Copyright: © 2022, The Author(s).

PY - 2023/2

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N2 - 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 (Φ) 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 “L1-regime” |α|<8π of the charge parameter α. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.

AB - 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 (Φ) 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 “L1-regime” |α|<8π of the charge parameter α. We also identify the solution with an infinite-dimensional diffusion process constructed by the Dirichlet form approach.

KW - Dirichlet form

KW - Gaussian multiplicative chaos

KW - Høegh-Krohn model

KW - Singular SPDE

KW - Stochastic quantization

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