Symmetry breaking, Ward identities, and the two-fluid model

We derive several important features of a Bose-condensed system, based on a diagrammatic analysis at finite temperatures. Firstly, the symmetry-breaking term necessary to describe Bose condensation is shown to give a rigorous basis for the fictitious gap argument of Gavoret and Nozières (1964). This puts their well-known results on a firm footing. Secondly, in the presence of a moving condensate with velocity $v_S$, the current carried by the noncondensate atoms is shown to be $({\rho }_S-{\mathrm{mn}}_o)v_S$. The results of this paper are direct consequences of various Ward identities which have been recently discussed for Bose-condensed systems.