Abstract
Using the idea of the quantum inverse scattering method, we introduce the operators B(x), C(x) and 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 B*(x) and 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 ⟨0|C(xN)⋯C(x1)B(y1)⋯B(yN)|0⟩ in the bc fermionic fields is the inverse of the correlation function ⟨0|C*(xN)⋯C*(x1)B*(y1)⋯B*(yN)|0⟩ in the charged free bosons.
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