particles is Interacting particles For interacting particles, the equation of motion becomes Hamiltonian for two particles in a vacuum The Darwin Hamiltonian for two particles in a vacuum is related to the Lagrangian by a Legendre transformation The Hamiltonian becomes Hamiltonian equations of motion The Hamiltonian equations of motion are and which yield and Note that the quantum mechanical Breit equation originally used the Darwin Lagrangian with the Darwin Hamiltonian as its classical starting point though the Breit equation would be better vindicated by the Wheeler–Feynman absorber theory and better yet quantum electrodynamics. See also Static forces and virtual-particle exchange Breit equation Wheeler–Feynman absorber theory References Magnetostatics Equations of physics