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Nonperturbative methods play an important role in quantum many-body systems,especially in situations with an interplay of continuum and bound states and/orlarge coupling strengths between the constituents. Employing the Luttinger-Wardfunctional (LWF) we have computed the equation of state (EoS) of thequark-gluon plasma (QGP) using fully dressed selfconsistent 1- and 2-bodypropagators. We first give an alternative derivation of our previously reportedresults for resumming the ladder diagram series of the LWF using a "matrix log"technique which accounts for dynamically formed bound and resonant states. Twotypes of solutions were found in selfconsistent fits to lattice-QCD data forthe EoS, heavy-quark free energy and quarkonium correlators: a strongly coupledscenario (SCS) with broad parton spectral functions and strong meson resonancesnear the transition temperature vs. a weakly coupled scenario (WCS) withwell-defined parton quasiparticles and weak meson resonances. Here, we discusshow these solutions can be distinguished by analyzing the pertinent transportproperties. We focus on the specific shear viscosity, $(4\pi )\eta/s$, and theheavy-quark diffusion coefficient, $(2\pi T) {\cal D}_s$, including its massdependence. At low temperatures, in the SCS, they turn out to be a factor of 2within their conjectured quantum lower bound, while they are a factor of 2-5larger in the WCS. At higher temperatures, the transport parameters of the twoscenarios approach each other. We propose the ratio $ (4\pi\eta/s)/(2\pi T{\cal D}_s )$ as a measure to distinguish the perturbative and strong-couplinglimits of 5/2 and 1, respectively.

Spectral and Transport Properties of Quark-Gluon Plasma in a Nonperturbative Approach