  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.
