A universal phase space for particles in Yang-Mills fields

Given a principal G-bundle P over M and a Hamiltonian G-space Q, one may construct the reduced symplectic manifold (T*PXQ)0. When a connection on P is chosen, this manifold becomes a bundle over T*M with fibre Q. It is shown that this bundle is precisely the phase space constructed by Sternberg for a classical particle in a Yang-Mills field. (Auth.)