Leading order calculation of shear viscosity in hot quantum electrodynamics from diagrammatic methods
Abstract
We compute the shear viscosity at leading order in hot quantum electrodynamics. Starting from the Kubo relation for shear viscosity, we use diagrammatic methods to write down the appropriate integral equations for bosonic and fermionic effective vertices. We also show how Ward identities can be used to put constraints on these integral equations. One of our main results is an equation relating the kernels of the integral equations with functional derivatives of the full selfenergy; it is similar to what is obtained with twoparticleirreducible effective action methods. However, since we use Ward identities as our starting point, gauge invariance is preserved. Using these constraints obtained from Ward identities and also power counting arguments, we select the necessary diagrams that must be resummed at leading order. This includes all noncollinear (corresponding to 2 to 2 scatterings) and collinear (corresponding to 1+N to 2+N collinear scatterings) rungs responsible for the LandauPomeranchukMigdal effect. We also show the equivalence between our integral equations obtained from quantum field theory and the linearized Boltzmann equations of Arnold, Moore and Yaffe obtained using effective kinetic theory.
 Publication:

Physical Review D
 Pub Date:
 November 2007
 DOI:
 10.1103/PhysRevD.76.105019
 arXiv:
 arXiv:0708.1631
 Bibcode:
 2007PhRvD..76j5019G
 Keywords:

 11.10.Wx;
 05.60.Gg;
 11.15.q;
 Finitetemperature field theory;
 Quantum transport;
 Gauge field theories;
 High Energy Physics  Phenomenology;
 Nuclear Theory
 EPrint:
 45 pages, 22 figures (note that figures 7 and 14 are downgraded in resolution to keep this submission under 1000kb, zoom to see them correctly)