  It can be shown that the bosonic degree of freedom of the tightly bound
on-site electron pairs could be separated as Schwinger bosons. This is
implemented by projecting the whole Hilbert space into the Hilbert subspace
spanned by states of two kinds of Schwinger bosons (to be called binon and
vacanon) subject to a constraint that these two kinds of bosonic quasiparticles
cannot occupy the same site. We argue that a binon is actually a kind of
quantum fluctuations of electron pairs, and a vacanon corresponds to a vacant
state. These two bosonic quasiparticles may be responsible for the
Bose-Einstein condensation (BEC) of the system associated with electron pairs.
These concepts are also applied to the attractive Hubbard model with strong
coupling, showing that it is quite useful. The relevance of the present
arguments to the existing theories associated with the BEC of electron pairs is
briefly commented.
