Geometric quantization of non-relativistic and relativistic Hamiltonian   mechanics
  We show that non-relativistic and relativistic mechanical systems on a configuration space Q can be seen as the conservative Dirac constraint systems with zero Hamiltonians on different subbundles of the same cotangent bundle T^*Q. The geometric quantization of this cotangent bundle under the vertical polarization leads to compatible covariant quantizations of non-relativistic and relativistic Hamiltonian mechanics. 
G.Giachetta, L.Mangiarotti, G.Sardanashvily