Since the conservation equations involve tensors, the Einstein summation convention will be used where repeated indices in a product indicate summation over those indices. Thus x ↦ ↦ x i and p ↦ ↦ p i = m v i , where v i is the particle velocity vector. Define A ( p i ) as some function of momentum p i only, which is conserved in a collision. Assume also that the force F i is a function of position only, and that f is zero for p i → → ± ± ∞ ∞ . Multiplying the Boltzmann equation by A and integrating over momentum yields four terms, which, using integration by parts, can be expressed as