  In this paper we study the Cauchy problem for the spatially homogeneous
relativistic Landau equation with Coulomb interactions. Despite it's physical
importance, this equation has not received a lot of mathematical attention we
think due to the extreme complexity of the relativistic structure of the kernel
of the collision operator. In this paper we first largely decompose the
structure of the relativistic Landau collision operator. After that we prove
the global Entropy dissipation estimate. Then we prove the propagation of any
polynomial moment for a weak solution. Lastly we prove the existence of a true
weak solution for a large class of initial data.
