The 2 - particle irreducible effective action in gauge theories

The goal of this paper is to develop the formalism of the two-particle irreducible (2PI) \cite{LW61} (or Cornwall - Jackiw - Tomboulis (CJT) \cite {CJT}) effective action (EA) in a way appropiate to its application to non equilibrium gauge theories. We hope this review article will stimulate new work into this field.Comment: 25 page

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

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.Comment: 30 pages. Accepted for publication in JPC

Macroscopic approximation to relativistic kinetic theory from a nonlinear closure

We use a macroscopic description of a system of relativistic particles based on adding a nonequilibrium tensor to the usual hydrodynamic variables. The nonequilibrium tensor is linked to relativistic kinetic theory through a nonlinear closure suggested by the Entropy Production Principle; the evolution equation is obtained by the method of moments, and together with energy-momentum conservation closes the system. Transport coefficients are chosen to reproduce second order fluid dynamics if gradients are small. We compare the resulting formalism to exact solutions of Boltzmann's equation in 0+1 dimensions and show that it tracks kinetic theory better than second order fluid dynamics.Comment: v2: 6 two-column pages, 2 figures. Corrected typos and a numerical error, and added reference

A hydrodynamic approach to QGP instabilities

We show that the usual linear analysis of QGP Weibel instabilities based on the Maxwell-Boltzmann equation may be reproduced in a purely hydrodynamic model. The latter is derived by the Entropy Production Variational Method from a transport equation including collisions, and can describe highly nonequilibrium flow. We find that, as expected, collisions slow down the growth of Weibel instabilities. Finally, we discuss the strong momentum anisotropy limit.Comment: 11 pages, no figures. v2: minor changes, added references. Accepted in Phys. Rev.