  We develop a bosonization technique for one-dimensional fermions out of
equilibrium. The approach is used to study a quantum wire attached to two
electrodes with arbitrary energy distributions. The non-equilibrium electron
Green function is expressed in terms of functional determinants of a
single-particle``counting'' operator with a time-dependent scattering phase.
The result reveals an intrinsic relation of dephasing and energy redistribution
in Luttinger-liquids to ``fractionalization'' of electron-hole excitations in
the tunneling process and at boundaries with leads.
