Removal of acceleration terms from the two-body Lagrangian to order c−4 in electromagnetic theory

Abstract

Starting with the acceleration-dependent Lagrangian to order c−4 for two charged bodies (with e1/m1 = e2/m2) in electromagnetic theory, we show how to correctly convert the acceleration-dependent terms in this Lagrangian into velocity- and coordinate-dependent terms by a procedure that we call the method of the double zero. From the resulting velocity-dependent Lagrangian we easily find the corresponding Hamiltonian and corresponding Hamiltonian and Lagrangian in center-of-mass coordinates. We also give the Ostrogradsky Hamiltonian.