96-652 T.Kojima, V.E.Korepin and N.A.Slavnov

Determinant representation for dynamical correlation functions of the Quantum nonlinear Schr\"odinger equation. (87K, LaTeX) Dec 10, 96

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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.

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