Two-particle irreducible effective action approach to nonlinear current-conserving approximations in driven systems

Abstract

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.

Wave propagation in non-Gaussian random media

“…In this paper we have casted the problem of scalar wave propagation in a random medium in a field theoretic language which connects it immediately to the larger body of work [73,75] addressed to similar problems in high energy physics and cosmology [57] and the theory of turbulence [76,77,78,79,80]. The advantages of the method, as compared with the straightforward approach of iterating the Dyson equation, are that it provides a partial resummation of the perturbative series which avoids overcounting and has energy conservation built in order by order [69]. As a sample of the power of the method we have analyzed the effect of non gaussian statistics on the mass and intensity operators.…”

“…The key to the power of the method is that the seeming complexity of dealing with a larger number of fields (auxiliary and ghost [67,68] fields on top of the physical ones) is overridden by the fact that the 2PI EA is built from Feynman graphs with no external legs and which are two-particle irreducible, meaning that they remain connected after cutting any two internal legs. The number of these graphs at any finite order in perturbation theory is small enough that the computational effort stays manageable, and their structure is so tightly constrained that it is possible to provide proofs of key features, such as flux conservation, at any order [69].…”

New method to calculate then-particle irreducible effective action

“…For scalar theories, one can define a 2-point function that satisfies Goldstone's theorem in the broken phase [18,19]. For QED, one can define n-point functions that obey Ward identities [20][21][22]. These symmetry constraints allow one to construct a renormalized theory that preserves the symmetries of the original theory [19,[23][24][25][26].…”

Towards next-to-leading order transport coefficients from the four-particle irreducible effective action

“…For scalar theories one can define a 2-point function that satisfies Goldstone's theorem in the broken phase [21,22]. For QED one can define n-point functions that obey traditional Ward identities [23,24]. These symmetry constraints allow one to construct a complete renormalization that preserves the symmetries of the original theory [22,[25][26][27][28].…”