  The standard theoretical basis for understanding superfluidity in Bose
systems was formulated by Beliaev in 1957, based on splitting the quantum field
operator into a macroscopically occupied condensate component and a
non-condensate component. This leads to a description of the condensate in
terms of a 'single-particle state', the so-called macroscopic wavefunction.
Since the discovery of Bose-condensed gases, an alternative theoretical picture
has been developed which is based on a 'coherent band' of classically occupied
states. This is often called the classical or c-field approach. The goal of
this chapter is to review the differences between the Beliaev broken symmetry
and c-field approach, and to argue that the c-field concept of a coherent
condensate band of states has problems as a description of Bose superfluidity.
However, the c-field idea of treating the lowest energy excitations classically
can be used to advantage to simplify calculations within the Beliaev
broken-symmetry formalism.
