2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56697We 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.18 pagesMathematical PhysicsHigh Energy Physics - TheoryQuantum PhysicsGeometric quantization of non-relativistic and relativistic Hamiltonian mechanicstext