Particle Production from Oscillating Scalar Field and Consistency of
  Boltzmann Equation
  Boltzmann equation plays important roles in particle cosmology in studying
the evolution of distribution functions (also called as occupation numbers) of
various particles. For the case of the decay of a scalar condensation $\phi$
into a pair of scalar particles (called $\chi$), we point out that the system
may not be well described by the Boltzmann equation when the occupation number
of $\chi$ becomes large even in the so-called narrow resonance regime. We study
the particle production including the possible enhancement due to a large
occupation number of the final state particle, known as the stimulated emission
or the parametric resonance. Based on the quantum field theory (QFT), we derive
a set of equations which directly govern the evolution of the distribution
function of $\chi$. Comparing the results of the QFT calculation and those from
the Boltzmann equation, we find non-agreements in some cases. In particular, in
the expanding Universe, the occupation number of $\chi$ based on the QFT may
differ by many orders of magnitude from that from the Boltzmann equation. We
also discuss a possible relation between the evolution equations based on the
QFT and the Boltzmann equation.
