  The relativistic quantum Boltzmann equation (or the relativistic
Uehling-Uhlenbeck equation) describes the dynamics of single-species
fast-moving quantum particles. With the recent development of the relativistic
quantum mechanics, the relativistic quantum Boltzmann equation has been widely
used in physics and engineering such as in the quantum collision experiments
and the simulations of electrons in graphene. In spite of such importance,
there has been no mathematical theory on the existence of solutions for the
relativistic quantum Boltzmann equation to the best of authors' knowledge. In
this paper, we prove the global existence of a unique classical solution to the
relativistic Boltzmann equation for both bosons and fermions when the initial
distribution is nearby a global equilibrium.
