Center of inertia and coordinate transformations in the post-Newtonian charged n-body problem in gravitation

We generalize the field theory propagator by finding a way to make it a function of some additional arbitrary parameters. Thus, it is now possible to obtain Lagrangians (which contain the propagator parameters) from field theory in a more general coordinate system than had previously been possible. We find the n-body (classical) Bazanski Lagrangian in this more general coordinate system and we give the relationship between the various coordinate systems by an n-body coordinate transformation involving the propagator parameters. We find the center of inertia for the case of the n-body Baszanski Lagrangian in the general coordinate system and find that the potential energy terms -Gm/sub i/m/sub j//r/sub i/j and e/sub i/e/sub j//r/sub i/j do not in general split equally between particles i and j as they do in the case of Bazanski coordinates. We also find the center of inertia for the case of the n-body (unchanged) post-Newtonian Lagrangian with parameterized post-Newtonian (PPN) parameters γ and β in standard coordinates, and show that the potential energy terms do split equally between a pair of particles