Transport equations including many-particle correlations for an   arbitrary quantum system. General formalism
  We present a new method to derive transport equations for quantum many-particle systems. This method uses an equation-of-motion technique and is applicable to systems with bosons and fermions, arbitrary interactions and time-dependent external fields. Using a cluster expansion of the r-particle density matrices the infinite hierarchy of equations of motion for many-particle expectation values is transposed into an equivalent one in terms of correlations. This new hierarchy permits a systematic breaking of the hierarchy at any order. Diagrams are derived for these transport equations. In a second paper the method is tested for exactly soluble electron-phonon models in one dimension. 
J. Fricke