Conformal symmetry for relativistic point particles: an addendum
  We extend the results of our previous work on the conformal invariant description of two relativistic point particles. We consider here the most general lagrangian by using a conformal tensor $h_{\mu\nu}$, transforming as a Wilson line, and that allows us to construct invariant expressions for velocities taken at two different space-time points. 
Roberto Casalbuoni and Joaquim Gomis
hep-th