Correlation functions of charged free boson and fermion systems

Abstract

Using the idea of the quantum inverse scattering method, we introduce the operators $\mathbf{B}(x),\mathbf{C}(x)$ and $\tilde{\mathbf{B}}(x),\tilde{\mathbf{C}}(x)$ 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 ${\mathbf{B}}^{\ast }(x)$ and ${\mathbf{C}}^{\ast }(x)$ 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 $⟨0|\mathbf{C}(x_N)\cdots \mathbf{C}(x_1)\mathbf{B}(y_1)\cdots$ $\mathbf{B}(y_N)|0⟩$ in the $bc$ fermionic fields is the inverse of the correlation function $⟨0|{\mathbf{C}}^{\ast }(x_N)\cdots {\mathbf{C}}^{\ast }(x_1){\mathbf{B}}^{\ast }(y_1)\cdots {\mathbf{B}}^{\ast }(y_N)|0⟩$ in the charged free bosons.

26 pages. Final version for J. Stat. Mech