Boltzmann equation for non-equilibrium particles and its application to
  non-thermal dark matter production
  We consider a scalar field (called $\phi$) which is very weakly coupled to
thermal bath, and study the evolution of its number density. We use the
Boltzmann equation derived from the Kadanoff-Baym equations, assuming that the
degrees of freedom in the thermal bath are well described as "quasi-particles."
When the widths of quasi-particles are negligible, the evolution of the number
density of $\phi$ is well governed by a simple Boltzmann equation, which
contains production rates and distribution functions both evaluated with
dispersion relations of quasi-particles with thermal masses. We pay particular
attention to the case that dark matter is non-thermally produced by the decay
of particles in thermal bath, to which the above mentioned formalism is
applicable. When the effects of thermal bath are properly included, the relic
abundance of dark matter may change by $O(10-100%)$ compared to the result
without taking account of thermal effects.
