Abstract
Using closed-time-path two-particle irreducible coarse-grained effective action (CTP 2PICGEA) techniques, we study the response of an open interacting electronic system totime-dependent external electromagnetic fields. We show that the CTP 2PI CGEA isinvariant under a simultaneous gauge transformation of the external field and the fullSchwinger–Keldysh propagator, and that this property holds even when the loopexpansion of the CTP 2PI CGEA is truncated at arbitrary order. The effective actionapproach provides a systematic way of calculating the propagator and responsefunctions of the system, via the Schwinger–Dyson equation and the Bethe–Salpeterequations, respectively. We show that, due to the invariance of the CTP 2PI CGEAunder external gauge transformations, the response functions calculated fromit satisfy the Ward–Takahashi hierarchy, thus warranting the conservation ofthe electronic current beyond the expectation value level. We also clarify theconnection between nonlinear response theory and the WT hierarchy, and discuss anexample of an ad hoc approximation that violates it. These findings may be usefulin the study of current fluctuations in correlated electronic pumping devices.
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