Dimensional reduction and symplectic reduction

The method of dimensional reduction as applied to pure Yang-Mills theory by Manton and Harnad et al. can be related to the symplectic-reduction scheme developed by Marsden and Weinstein when applied to the phase space for a «classical» particle moving in the presence of a Yang-Mills field. If the data satisfy the appropriate conditions, one can use a technique similar to the collective motion to integrate the equations of motion of the particle.