Φ^4_3 Theory from Many-Body Quantum Gibbs States

Explore the rigorous mathematical derivation of Φ^4_3 measure on the torus as a limit of quantum Gibbs states in this 51-minute conference talk. Learn how the limiting classical measure describes the critical behavior of an interacting Bose gas just above the Bose–Einstein phase transition. Discover the key challenge of approximating the local Φ^4_3 theory using a Hartree measure with nonlocal interaction, and examine how uniform estimates on the Hartree measure are achieved through techniques from stochastic quantization and paracontrolled calculus. Understand the connection to quantum problems through variational approaches, and see how recent correlation inequalities enable refined analysis leading to quantitative convergence of quantum correlation functions to those of the Hartree classical field. Gain insights into advanced mathematical physics concepts bridging quantum many-body systems and classical field theory.