  We define the "BEC state" to be the many-body wavefunction where all
particles are in the same one-body state. Using an argument analogous to
Anderson's Orthogonality Catastrophe, we argue that for interacting particles
the amplitude of the BEC state within the many-body wavefunction goes to zero
in the thermodynamic limit. This does not mean that there is no condensate.
However, we argue that, if the excitations satisfy the Landau criterion, then
the absence of a finite amplitude for the BEC state, or the absence of a
condensate, do not prevent the definition of the phase function \phi, from
which the superfluid velocity follows.
