T.Kojima, V.E.Korepin and N.A.Slavnov
Determinant representation for dynamical correlation
functions of the  Quantum nonlinear Schr\"odinger equation.
(87K, LaTeX)

ABSTRACT.  Painlev\'e analysis of correlation functions of the impenetrable Bose gas
by M.~Jimbo, T.~Miwa, Y.~M\^ori and M.~Sato \cite{JMMS} was based on the 
determinant representation of these correlation functions obtained
by A.~Lenard \cite{Len}. The impenetrable Bose gas is the free 
fermionic case of
the quantum nonlinear Schr\"odinger equation.
In this paper we generalize the Lenard determinant representation
for $\langle\psi(0,0)\psi^\dagger(x,t)\rangle$ to the non-free fermionic case.
We also include time and temperature dependence. In 
forthcoming publications we shall perform
 the JMMS analysis of this correlation function. This will give
us a completely integrable equation and asymptotic for 
the quantum correlation function of interacting fermions.