  The foundation for the theory of correlation functions of exactly solvable
models is determinant representation. Determinant representation permit to
describe correlation functions by classical completely integrable differential
equations [Barough, McCoy, Wu]. In this paper we show that determinant
represents works not only for free fermionic models. We obtained determinant
representation for the correlation function $<\psi(0,0)\psi^\dagger(x,t)>$ of
the quantum nonlinear Schr\"odinger equation, out of free fermionic point. In
the forthcoming publications we shall derive completely integrable equation and
asymptotic for the quantum correlation function of this model of interacting
fermions.
