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.