Hamiltonian of a slightly relativistic plasma

In the past, treatments of plasma to order v²/c², where v is the thermal speed of the particles, have relied on a Lagrangian formalism or on coarse graining techniques. It is shown that a Hamiltonian formulation where only particle degrees of freedom are considered is possible and a Hamiltonian to order v²/c² is obtained. This Hamiltonian is valid within the limits of the random phase approximation.