Abstract
The description of thermal or non-equilibrium systems necessitates a quantum field theory which differs from the usual approach in two aspects: 1.The Hilbert space is doubled; 2.Stable quasi-particles do not exist in interacting systems. A mini-review of these two aspects is given from a practical viewpoint including two applications. For thermal states it is shown how infrared divergences occuring in perturbative quasi-particle theories are avoided, whereas for non-equilibrium states a memory effect is shown to arise in the thermalization.
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