Speaker: 朱蓉禅教授，北京理工大学

Inviter: 中国科学院数学院学术报告会组委

Title: $\Phi^4_3$ Theory from many-body quantum Gibbs states

Language: Chinese

Time & Venue: 2025.11.21 10:40-11:50 数学院南楼N204（数学院交流报告会）

Abstract: We derive the $\Phi^4_3$ measure on the torus as a rigorous limit of the quantum Gibbs state of an interacting Bose gas, where the limiting classical measure describes the critical behavior of the Bose gas just above the Bose--Einstein phase transition. Since the quantum problem is typically formulated using a nonlocal interaction potential, a key challenge is to approximate the local $\Phi^4_3$ theory by a Hartree measure with a nonlocal interaction. This requires uniform estimates on the Hartree measure, which are achieved using techniques from recent development on stochastic quantization and paracontrolled calculus. The connection to the quantum problem is then established by applying the variational approach and deriving a quantitative convergence of the quantum correlation functions to those of the Hartree classical field.