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An approach is proposed to analyse an interacting bosonic system using two-time temperature Green’s functions on the collective variables. Two systems are studied: liquid helium-4 and the Yukawa Bose liquid being a model of the nuclear matter. The suggested decoupling in the equations of motion for Green’s functions yields a good description of the elementary excitation spectrum in the long-wavelength limit.

A Note on the Calculation of the Long-Wavelength Limit of the Bosonic Excitation Spectrum