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Geometric quantization of non-relativistic and relativistic Hamiltonian mechanics

G. Giachetta·L. Mangiarotti·G. Sardanashvily
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Abstract

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.

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G. Giachetta, L. Mangiarotti, G. Sardanashvily. 2000-12-14. Geometric quantization of non-relativistic and relativistic Hamiltonian mechanics. https://arxiv.org/abs/math-ph/0012030

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