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We find that correlation functions at one dimension are crucially affected bythe curvature of the bare single particle spectrum. Parabolic curvature leadsto two closely related phenomena: the Green's function exhibits oscillation (asa function of the coordinate), while the polarization operator acquires supportin part of the frequency-momentum plane. We calculated the Green's functionusing the WKB approximation for collective variables theory\cite{JevickiSakita}. Within this approach, the single particle Green'sfunction is related to a quantum soliton \cite{Polychronakos}. The finitesupport of the polarization operator is due to periodic density waves

Green’s function of quasiparticles in Calogero model and quantum hydrodynamics