Classical dynamics of particles with non-abelian gauge charges

The classical dynamics of particles with (non-)abelian charges and spin moving on curved manifolds is established in the Poisson-Hamilton framework. Equations of motion are derived for the minimal quadratic Hamiltonian and some extensions involving spin-dependent interactions. It is shown that these equations of motion coincide with the consistency conditions for current and energy-momentum conservation. The classical equations cannot be derived from an action principle without extending the model. One way to overcome this problem is the introduction of anticommuting Grassmann co-ordinates. A systematic derivation of constants of motion based on symmetries of the background fields is presented.