Quantum dissipation

We discuss some aspects of dissipation in quantum field theory starting from the example of the quantum mechanical damped harmonic oscillator. We show that the set of states of the system splits into unitarily inequivalent representations of the canonical commutation relations. At quantum level the irreversibility of time evolution is expressed as tunneling among the unitarily inequivalent representations. Statistical and thermodynamical properties of the formalism are analysed and canonical quantization is shown to lead to time dependent SU(1, 1) coherent states, well known in high energy physics as well as in quantum optics and thermal field theory.