Volume 79, Number 6, September 2007
Article Number 60002
Number of page(s) 3
Section General
Published online 21 August 2007
EPL, 79 (2007) 60002
DOI: 10.1209/0295-5075/79/60002

The exact Darwin Lagrangian

H. Essén

Department of Mechanics, KTH - SE-100 44 Stockholm, Sweden

received 2 July 2007; accepted in final form 29 July 2007; published September 2007
published online 21 August 2007

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.

03.50.De - Classical electromagnetism, Maxwell equations.
11.10.Ef - Lagrangian and Hamiltonian approach.

© Europhysics Letters Association 2007