Transport Coefficients and nPI Methods

TL;DR

This paper discusses how nPI effective actions can be used to compute transport coefficients like electrical conductivity and shear viscosity in quantum field theories, highlighting the advantages of this approach for systematic higher-order calculations.

Contribution

It demonstrates that the full leading order transport coefficients are contained in the re-summed nPI 3-loop effective action and suggests extending this to higher orders with 4-loop 4PI actions.

Findings

Leading order electrical conductivity and shear viscosity obtained from 3PI effective action.

Integral equations for shear viscosity derived in scalar theories with cubic and quartic interactions.

Framework proposed for calculating next-to-leading order transport coefficients.

Abstract

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 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 and suggests that one can calculate the next-to-leading contribution to transport coefficients from the 4-loop 4PI effective action. The integral equations have been derived for shear viscosity for a scalar theory with cubic and quartic interactions, with a non-vanishing field expectation value. We review these results, and explain how the calculation could be done at higher orders.