Feynman's Nobel classical electrodynamics action

In his Nobel lecture Feynman describes an electrodynamic action between a set of particles (equation 1, one third way thru lecture):

http://www.nobelprize.org/nobel_priz...n-lecture.html

The action is in 4-vector form.

I wonder if someone could do me a favour and re-express the action just for a pair of particles in 3-vector form?

I presume the action is related to the Darwin Lagrangian. The main difference between them is that in the Feynman action each particle has its own proper time whereas the Darwin lagrangian is expressed in a universal time.

Thanks,

John