The classical dynamics of particles with (non-)abelian charges and Restoration treatment 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 Candles Grassmann co-ordinates.A systematic derivation of constants of motion based on symmetries of the background fields is presented.