Unique Canonical Representation of the Inhomogeneous Lorentz Group in Relativistic Particle Dynamics

The Lie-K\"onigs theorem has been sharpened to consider the question of the canonical representation of symmetry groups of even-order differential equations. An application to instantaneous action-at-a-distance relativistic mechanics yields the existence and uniqueness of a Hamiltonian formulation within the framework of the canonical representations of the Lorentz group.