Non-Markovian source term for particle production by a self-interacting   scalar field in the large-N approximation
  The particle production in the self-interacting N-component complex scalar field theory is studied at large N. A non-Markovian source term that includes all higher order back-reaction and collision effects is derived. The kinetic amplitudes accounting for the change in the particle number density caused by collisions are obtained. It is shown that the production of particles is symmetric in the momentum space. The problem of renormalization is briefly discussed. 
Fuad M. Saradzhev