  Based on the quasiparticle model of the quark-gluon plasma (QGP), a color
quantum path-integral Monte-Carlo (PIMC) method for calculation of
thermodynamic properties and -- closely related to the latter -- a Wigner
dynamics method for calculation of transport properties of the QGP are
formulated. The QGP partition function is presented in the form of a color path
integral with a new relativistic measure instead of the Gaussian one
traditionally used in the Feynman-Wiener path integral. It is shown that the
PIMC method is able to reproduce the lattice QCD equation of state at zero
baryon chemical potential at realistic model parameters (i.e. quasiparticle
masses and coupling constant) and also yields valuable insight into the
internal structure of the QGP. Our results indicate that the QGP reveals
quantum liquid-like (rather than gas-like) properties up to the highest
considered temperature of 525 MeV. The pair distribution functions clearly
reflect the existence of gluon-gluon bound states, i.e. glueballs, at
temperatures just above the phase transition, while meson-like $q\bar{q}$ bound
states are not found. The calculated self-diffusion coefficient agrees well
with some estimates of the heavy-quark diffusion constant available from recent
lattice data and also with an analysis of heavy-quark quenching in experiments
on ultrarelativistic heavy ion collisions, however, appreciably exceeds other
estimates. The lattice and heavy-quark-quenching results on the heavy-quark
diffusion are still rather diverse. The obtained results for the shear
viscosity are in the range of those deduced from an analysis of the
experimental elliptic flow in ultrarelativistic heavy ions collisions, i.e. in
terms the viscosity-to-entropy ratio, $1/4\pi < \eta/S < 2.5/4\pi$, in the
temperature range from 170 to 440 MeV.
