Using the idea of the quantum inverse scattering method, we introduce the operators $mathbf{B}(x), mathbf{C}(x)$ and $mathbf{tilde{B}}(x), mathbf{tilde{C}}(x)$ corresponding to the off-diagonal entries of the monodromy matrix $T$ for the phase model and $i$-boson model in terms of bc fermions and neutral fermions respectively, thus giving alternative treatment of the KP and BKP hierarchies. We also introduce analogous operators $mathbf{B}^{*}(x)$ and $mathbf{C}^{*}(x)$ for the charged free boson system and show that they are in complete analogy to those of $bc$ fermionic fields. It is proved that the correlation function $langle 0|mathbf{C}(x_N)cdotsmathbf{C}(x_1)mathbf{B}(y_1)cdots $ $mathbf{B}(y_N)|0rangle$ in the $bc$ fermionic fields is the inverse of the correlation function $langle 0|mathbf{C}^{*}(x_N)cdotsmathbf{C}^{*}(x_1)mathbf{B}^{*}(y_1)cdots mathbf{B}^{*}(y_N)|0rangle$ in the charged free bosons.
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