I have been wondering the relation between Higgs BEC and Higgs field. During reheating of the universe, people always claim the energy density of inflaton drops down like massive particles without pressure. So that energy can be interpreted as inflaton condensate. But are they really the same thing? For a scalar field in general, there is potential energy. Can we always say the energy in the potential energy belongs to the condensate?
A remotely relevant question is, what's the relation between photons and classical electromagnetic field? Do photon, W/Z boson in SM condense?