Phonon Spectrum of a Degenerate System of Bosons at Finite Temperature

A new set of quasi· particle operators are introduced into the theory of a degenerate system of bosons in which the depletion of the condensate is appreciable. These operators are related by a nonlinear canonical transformation to the density fluctuation operators and their canonical conjugates. T.he quasiparticles have a temperature dependent phonon spectrum. They incorporate the interaction between bbsons with non-zero momenta. In the limit as the density of the condensate approaches zero, tYte proposed theory is reduced to the Hartree-Fock theory for a nondegenerate system.