Derivation of $\Phi^4_3$ theory from many-body quantum mechanics

Phan Thanh Nam (LMU Munich)

Nov 26. 2025, 11:45 — 12:25

We will discuss a rigorous derivation of the classical $\Phi^4_3$ measure as a semiclassical limit of the quantum Gibbs state for an interacting Bose gas. Consequently, we show that the classical field theory is appropriate to capture the formation of Bose–Einstein condensation just above the critical temperature. The proof combines techniques from both stochastic quantization and many-body quantum mechanics, including paracontrolled calculus, variational principles, and correlation inequalities. The talk is based on joint work with Rongchan Zhu and Xiangchan Zhu. 
 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Quantum Many-body Systems and Bose-Einstein Condensation: A Mathematical Physics Perspective (Workshop)
Organizer(s):
Serena Cenatiempo (Gran Sasso Science Institute, L'Aquila)
Christian Hainzl (LMU Munich)
Robert Seiringer (ISTA, Klosterneuburg)