Curvature in phase space

The purpose of this thesis is to make an examination of the Maxwell-Boltzmann transport equation and then to suggest methods of deriving the collision terms by fundamental methods. This approach differs from the usual approach in that, classically, the source terms of the Boltzmann equation are obtained by heuristic methods; whereas, herein the collision source terms are induced by curvature of phase space. The most important curvature example of this paper shows that the subspace of free particle motion in an assumedly flat phase space is necessarily curved.