Hidden symmetries in a gauge covariant approach, Hamiltonian reduction   and oxidation
  Hidden symmetries in a covariant Hamiltonian formulation are investigated involving gauge covariant equations of motion. The special role of the Stackel-Killing tensors is pointed out. A reduction procedure is used to reduce the original phase space to another one in which the symmetries are divided out. The reverse of the reduction procedure is done by stages performing the unfolding of the gauge transformation followed by the Eisenhart lift in connection with scalar potentials. 
Mihai Visinescu
hep-th