  Non-equilibrium bosonization technique is used to study current fluctuations
of interacting electrons in a single-channel quantum wire representing a
Luttinger liquid (LL) conductor. An exact expression for the full counting
statistics of the transmitted charge is derived. It is given by Fredholm
determinant of the counting operator with a time dependent scattering phase.
The result has a form of counting statistics of non-interacting particles with
fractional charges, induced by scattering off the boundaries between the LL
wire and the non-interacting leads.
