Leading Order QED Electrical Conductivity from the 3PI Effective Action

In this article we study the electrical conductivity in QED using the resummed 3PI effective action. We work to 3-loop order in the effective action. We show that the resulting expression for the conductivity is explicitly gauge invariant, and that the integral equations that resum the pinching and colinear contributions are produced naturally by the formalism. All leading order terms are included, without the need for any kind of power counting arguments.Comment: 10 pages, 15 figure

Three-Point Functions at Finite Temperature

We study 3-point functions at finite temperature in the closed time path formalism. We give a general decomposition of the eight component tensor in terms of seven vertex functions. We derive a spectral representation for these seven functions in terms of two independent real spectral functions. We derive relationships between the seven functions and obtain a representation of the vertex tensor that greatly simplifies calculations in real time.Comment: 21 pages LaTeX; one ps-figure; Revised version, contains more references and discussio

Next-to-Leading Order Transport Coefficients from the Four-Particle Irreducible Effective Action

Transport coefficients can be obtained from 2-point correlators using the Kubo formulae. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the re-summed 2-point function that is obtained from the 3-loop 3PI re-summed effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation. In this article we study the 4-loop 4PI effective action for a scalar theory with cubic and quartic interactions in the presence of spontaneous symmetry breaking. We obtain a set of integral equations that determine the re-summed 2-point vertex function. A next-to-leading order contribution to the viscosity could be obtained from this set of coupled equations.Comment: 24 pages, 18 figures. Added references and minor rewordings: published versio

The soft fermion dispersion relation at next-to-leading order in hot QED

We study next-to-leading order contributions to the soft static fermion dispersion relation in hot QED. We derive an expression for the complete next-to-leading order contribution to the retarded fermion self-energy. The real and imaginary parts of this expression give the next-to-leading order contributions to the mass and damping rate of the fermionic quasi-particle. Many of the terms that are expected to contribute according to the traditional power counting argument are actually subleading. We explain why the power counting method over estimates the contribution from these terms. For the electron damping rate in QED we obtain: $\gamma_{QED} = \frac{e^2 T}{4\pi}(2.70)$. We check our method by calculating the next-to-leading order contribution to the damping rate for the case of QCD with two flavours and three coulours. Our result agrees with the result obtained previously in the literature. The numerical evaluation of the nlo contribution to the mass is left to a future publication.Comment: 15 pages, 5 figure

KMS conditions for 4-point Green functions at finite temperature

We study the 4-point function in the Keldysh formalism of the closed time path formulation of real time finite temperature field theory. We derive the KMS conditions for these functions and discuss the number of 4-point functions that are independent. We define a set of `physical' functions which are linear combinations of the usual Keldysh functions. We show that these functions satisfy simple KMS conditions. In addition, we consider a set of integral equations which represent a resummation of ladder graphs. We show that these integral equations decouple when one uses the physical functions that we have defined. We discuss the generalization of these results to QED.Comment: 17 pages in Revtex with 2 figure