  We extend a path-integral approach to bosonization previously developed in
the framework of equilibrium Quantum Field Theories, to the case in which
time-dependent interactions are taken into account. In particular we consider a
non covariant version of the Thirring model in the presence of a dynamic
barrier at zero temperature. By using the Closed Time Path (Schwinger-Keldysh)
formalism, we compute the Green's function and the Total Energy Density of the
system. Since our model contains the Tomonaga Luttinger model as a particular
case, we make contact with recent results on non-equilibrium electronic
systems.
