  Using closed-time path two-particle irreducible coarse-grained effective
action (CTP 2PI CGEA) techniques, we study the response of an open interacting
electronic system to time-dependent external electromagnetic fields. We show
that the CTP 2PI CGEA is invariant under a simultaneous gauge transformation of
the external field and the full Schwinger-Keldysh propagator, and that this
property holds even when the loop expansion of the CTP 2PI CGEA is truncated at
arbitrary order. The effective action approach provides a systematic way of
calculating the propagator and response functions of the system, via the
Schwinger-Dyson equation and the Bethe-Salpeter equations, respectively. We
show that, due to the invariance of the CTP 2PI CGEA under external gauge
transformations, the response functions calculated from it satisfy the
Ward-Takahashi hierarchy, thus warranting the conservation of the electronic
current beyond the expectation value level. We also clarify the connection
between nonlinear response theory and the WT hierarchy, and discuss an example
of an ad hoc approximation that violate it. These findings may be useful in the
study of current fluctuations in correlated electronic pumping devices.
