Abstract
In the first part, a weakly interacting Boson system is considered. TheFradkin’s (1) formula for the internal energy is deduced and explicit calculation is made for propagators. The final energy spectrum allows us to conclude that in this system, or, in the region of validity of the Hartree approximation for the two-body propagator, cannot exist terms linear in momentumk. (The phonon part of Landau spectrum). The second part is devoted to the calculation of the partition function for the same system of bosons, when the temperature is not too low.
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