  We develop an operator-based approach to the problem of Luttinger liquid
conductor in a non-equilibrium stationary state. We show that the
coherent-state many-body fermionic density matrix as well as all fermionic
correlation functions out of equilibrium are given by one-dimensional
functional determinants of the Fredholm type. Thus, the model constitutes a
remarkable example of a many-body problem where all the correlation functions
can be evaluated exactly. On the basis of the general formalism we investigate
four-point correlation functions of the fermions coming out of the Luttinger
liquid wire. Obtained correlations in the fermionic distribution functions
represent the combined effect of interaction and non-equilibrium conditions.
