TY - JOUR
T1 - Stochastic quantization associated with the exp (Φ) 2 -quantum field model driven by space-time white noise on the torus
AU - Hoshino, Masato
AU - Kawabi, Hiroshi
AU - Kusuoka, Seiichiro
N1 - Funding Information:
The authors thank anonymous referees for helpful suggestions that improved the quality of the present paper. This work was partially supported by JSPS KAKENHI Grant Numbers 17K05300, 17K14204 and 19K14556.
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2021/3
Y1 - 2021/3
N2 - 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 it with an infinite-dimensional diffusion process, which has been constructed by the Dirichlet form approach.
AB - 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 it with an infinite-dimensional diffusion process, which has been constructed by the Dirichlet form approach.
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U2 - 10.1007/s00028-020-00583-0
DO - 10.1007/s00028-020-00583-0
M3 - Article
AN - SCOPUS:85085894068
SN - 1424-3199
VL - 21
SP - 339
EP - 375
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
IS - 1
ER -