DETERMINANT REPRESENTATION FOR DYNAMICAL CORRELATION-FUNCTIONS OF THEQUANTUM NONLINEAR SCHRODINGER-EQUATION

Painleve analysis of correlation functions of the impenetrable Bose ga s by M. Jimbo, T. Miwa, Y. Mori and M. Sate [1] was based on the deter minant representation of these correlation functions obtained by A. Le nard [2]. The impenetrable Bose gas is the free fermionic case of the quantum nonlinear Schrodinger equation, In this paper we generalize th e Lenard determinant representation for [psi(0,0)psi dagger (x, t)] to the non-free fermionic case. We also include time and temeprature dep endence. In forthcoming publications we shall perform the JMMS analysi s of this correlationl function. This will give us a completely integr able equation and asymptotic for the quantum correlation function of i nteracting fermions.