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The foundation for the theory of correlation functions of exactly solvablemodels is determinant representation. Determinant representation permit todescribe correlation functions by classical completely integrable differentialequations [Barough, McCoy, Wu]. In this paper we show that determinantrepresents works not only for free fermionic models. We obtained determinantrepresentation for the correlation function $<\psi(0,0)\psi^\dagger(x,t)>$ ofthe quantum nonlinear Schr\"odinger equation, out of free fermionic point. Inthe forthcoming publications we shall derive completely integrable equation andasymptotic for the quantum correlation function of this model of interactingfermions.Comment: LaTEX file, 35 pages, to appear in C.M.P. (1997

Determinant Representation for Dynamical Correlation Functions of the Quantum Nonlinear Schrödinger Equation