Since the pioneering work of Dobrushin--Shlosman (1975), the phenomenon of absense of spontaneous symmetry-breakdown in 2D systems of Statistical Mechanics attracted subtantial attention. Recently, there has been progress achieved for various classes of quantum systems. In the talk I will report new results claiming translation-invariance of 2D quantum boson gas. The techniques are based on the Feynman-Kac representation of the quantum Gibbs ensemble in terms of integrals over Brownian trajectories.