dorsal/arxiv
View SchemaCovariant geometric quantization of non-relativistic Hamiltonian mechanics
| Authors | G. Giachetta, L. Mangiarotti, G. Sardanashvily |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0012036 |
| URL | https://arxiv.org/abs/quant-ph/0012036 |
Abstract
We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. The goal is the Schrodinger representation of V^*Q. We show that this quantization is equivalent to the fibrewise quantization of symplectic fibres of V^*Q -> R, that makes the quantum algebra of non-relativistic mechanics an instantwise algebra. Quantization of the classical evolution equation defines a connection on this instantwise algebra, which provides quantum evolution in non-relativistic mechanics as a parallel transport along time.
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"date_created": "2026-03-02T18:01:42.652000Z",
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"abstract": "We provide geometric quantization of the vertical cotangent bundle V^*Q\nequipped with the canonical Poisson structure. This is a momentum phase space\nof non-relativistic mechanics with the configuration bundle Q -\u003e R. The goal is\nthe Schrodinger representation of V^*Q. We show that this quantization is\nequivalent to the fibrewise quantization of symplectic fibres of V^*Q -\u003e R,\nthat makes the quantum algebra of non-relativistic mechanics an instantwise\nalgebra. Quantization of the classical evolution equation defines a connection\non this instantwise algebra, which provides quantum evolution in\nnon-relativistic mechanics as a parallel transport along time.",
"arxiv_id": "quant-ph/0012036",
"authors": [
"G. Giachetta",
"L. Mangiarotti",
"G. Sardanashvily"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"title": "Covariant geometric quantization of non-relativistic Hamiltonian mechanics",
"url": "https://arxiv.org/abs/quant-ph/0012036"
},
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