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 relativistic quantum mechanics, the relativistic quantum Boltzmann equation has been widely used in physics and engineering, for example in the quantum collision experiments and the simulations of electrons in graphene. In spite of such importance, there has, to the best of our knowledge, been no mathematical theory on the existence of solutions to the relativistic quantum Boltzmann equation. 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.

相对论量子玻尔兹曼方程（或相对论Uehling–Uhlenbeck方程）描述了单物种快速移动量子粒子的动力学。随着相对论量子力学的最新发展，相对论量子玻耳兹曼方程已被广泛用于物理和工程领域，例如在量子碰撞实验和石墨烯中电子的模拟中。尽管具有如此重要的意义，但据我们所知，还没有关于相对论量子玻耳兹曼方程解存在性的数学理论。在本文中，我们证明了当初始分布在全局平衡附近时，玻色子和费米子相对论玻尔兹曼方程的唯一经典解的全局存在性。