  We point out a basic ambiguity in the $p \to 0$ limit of the connected
propagator in a spontaneously broken phase. This may represent an indication
that the conventional singlet Higgs boson, rather than being a purely massive
field, might have a gap-less branch. This would dominate the energy spectrum
for ${\bf{p}} \to 0$ and give rise to a very weak, long-range force. The
natural interpretation is in terms of density fluctuations of the `Higgs
condensate': in the region of very long wavelengths, infinitely larger than the
Fermi scale, it cannot be treated as a purely classical c-number field.
