Subdynamics of relevant observables : a field theoretical approach

An approach to the description of subdynamics inside the nonrelativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory derivation of the subdynamics of a microsystem interacting through collisions with a macrosystem is given, leading to a master equation expressed in terms of the operator-valued dynamic structure factor, a two-point correlation function which compactly takes the statistical mechanics properties of the macrosystem into account. For the case of a free quantum gas the dynamic structure factor can be exactly calculated and in the long wavelength limit a Fokker\u2013Planck equation for the description of quantum dissipation and in particular quantum Brownian motion is obtained, where peculiar corrections due to quantum statistics can be put into evidence