  In this letter we derive an action principle for Coulomb collisions in
plasmas. Although no natural Lagrangian exists for the Landau-Fokker-Planck
equation, an Eulerian variational formulation is found considering the system
of partial differential equations that couple the distribution function and the
Rosenbluth potentials. Exact conservation laws are derived after generalizing
the energy-momentum stress tensor for second order Lagrangians and, in the case
of a test-particle population in a given plasma background, the action
principle is shown to correspond to the Langevin equation for individual
particles. Being suitable for discretization, the presented action allows
construction of variational integrators. Numerical implementation is left for a
future study.
