Partial self-energy parts of Kadanoff-Baym

Abstract

Abstract The fundamental equations of Kadanoff and Baym (K-B) relating Green's functions ( g > and g ) and self-energy parts (Σ > and Σ ) are derived directly without going through the technique of imaginary-time Green's function. Explicit definitions for Σ > and Σ are given in terms of diagrams. The derivation based on the perturbation theory suggests the possible use of Green's function defined with a more general density operator than the equilibrium one e.g. for the problem of approach to equilibrium. The method of K-B is compared with the existing theories of irreversible processes developed by different authors. The method agrees in principles with the perturbation method of Fujita. The self-energy parts (Σ , Σ > ) are related to ( W ιι′ G ι ) of Van Hove and ψ( z ) of Prigogine-Resibois both responsible for localized collision processes but they contain also the information about the previous history of particles depending on a given initial condition. The separation of these apparently different processes is however one of the main points in the theories of Van Hove and Prigogine-Resibois.