The w*-algebra in the standard representation isused to define a vector space for representations of Liealgebras. The Poincare group is studied as inthermofield dynamics (TFD) with the result that thenotion of phase space is introduced from the structureof the Poincare-Lie algebra. The basis of quantum-fieldkinetic theory is analyzed in association with TFD. Asa particular case, the Juttner distribution is derived.