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

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
JournalProbability Theory and Related Fields
DOIs
Publication statusAccepted/In press - 2022

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

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