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)\cdots\mathbf{C}(x_1)\mathbf{B}(y_1)\cdots $ $\mathbf{B}(y_N)|0\rangle$ in the $bc$ fermionic fields is the inverse of the correlation function $\langle 0|\mathbf{C}^{*}(x_N)\cdots\mathbf{C}^{*}(x_1)\mathbf{B}^{*}(y_1)\cdots \mathbf{B}^{*}(y_N)|0\rangle$ in the charged free bosons.

中文翻译：

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带电自由玻色子和费米子系统的相关函数

利用量子逆散射方法的思想，我们引入了算子 $\mathbf{B}(x), \mathbf{C}(x)$ 和 $\mathbf{\tilde{B}}(x), \mathbf {\tilde{C}}(x)$分别对应bc费米子和中性费米子的相位模型和$i$-玻色子模型的单项矩阵$T$的非对角线项，从而给出替代处理KP 和 BKP 层次结构。我们还为带电自由玻色子系统引入了类似的算子 $\mathbf{B}^{*}(x)$ 和 $\mathbf{C}^{*}(x)$ 并表明它们完全类似于那些$bc$ 费米子场。