The exact Darwin lagrangian

Darwin (1920) noted that when radiation can be neglected it should be possible to eliminate the radiation degrees of freedom from the action of classical electrodynamics and keep the discrete particle degrees of freedom only. Darwin derived his well-known Lagrangian by series expansion in v/c keeping terms up to order (v/c)(2). Since radiation is due to acceleration the assumption of low speed should not be necessary. A Lagrangian is suggested that neglects radiation without assuming low speed. It cures deficiencies of the Darwin Lagrangian in the ultra-relativistic regime. Copyright (C) EPLA, 2007.