  An alternative formalism that does not require the assumption of the
deconfinement phase of a U(1) gauge field is proposed for the slave particle
mean field theory. Starting form the spin-fermion model, a spinon field, which
is either fermion or boson, is introduced to represent the localized spin
moment. We find a d-wave superconductive state in the mean field theory in the
case of the fermion representation of the localized spin moment that
corresponds to the slave boson mean field theory of the t-J model, whereas the
d-wave superconductive state is absent in case of the Schwinger boson
representation of the localized spin moments.
