  The Fokker action governing the motion of compact binary systems without
spins is derived in harmonic coordinates at the fourth post-Newtonian
approximation (4PN) of general relativity. Dimensional regularization is used
for treating the local ultraviolet (UV) divergences associated with point
particles, followed by a renormalization of the poles into a redefinition of
the trajectories of the point masses. Effects at the 4PN order associated with
wave tails propagating at infinity are included consistently at the level of
the action. A finite part procedure based on analytic continuation deals with
the infrared (IR) divergencies at spatial infinity, which are shown to be fully
consistent with the presence of near-zone tails. Our end result at 4PN order is
Lorentz invariant and has the correct self-force limit for the energy of
circular orbits. However, we find that it differs from the recently published
result derived within the ADM Hamiltonian formulation of general relativity [T.
Damour, P. Jaranowski, and G. Sch\"afer, Phys. Rev. D 89, 064058 (2014)]. More
work is needed to understand this discrepancy.
