Covariant spin kinetic theory I: collisionless limit

We develop a covariant kinetic theory for massive fermions in a curved spacetime and an external electromagnetic field based on quantum field theory. We derive four coupled semi-classical kinetic equations accurate to begin{document}$O(hbar)$end{document}, which describe the transports of particle number and spin degrees of freedom. The relationship with chiral kinetic theory is discussed. As an application, we study spin polarization in the presence of finite Riemann curvature and an electromagnetic field in both local and global equilibrium states.