Geometric quantization of non-relativistic and relativistic Hamiltonian mechanics
GIOVANNI GIACHETTA, Luigi Mangiarotti, Gennadi Aleksandrovich Sardanashvily
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.
arXiv:math-ph/0012030•Dec 14, 2000•0 citations