Interaction Vertex for Classical Spinning Particles

We consider a model of the classical spinning particle in which the coadjoint orbits of the Poincare group are parametrized by two pairs of canonically conjugate four vectors, one representing the standard position and momentum variables and the other which encodes the spinning degrees of freedom. This "Dual Phase Space Model" is shown to be a consistent theory of both massive and massless particles and allows for coupling to background fields such as electromagnetism. The on-shell action is derived and shown to be a sum of two terms, one associated with motion in spacetime and the other with motion in "spin space." Interactions between spinning particles are studied and a necessary and sufficient condition for consistency of a three-point vertex is established.