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Covariant geometric quantization of non-relativistic Hamiltonian mechanics

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G.Giachetta, L.Mangiarotti, G.Sardanashvily

Quantum Physics · Submitted 7 Dec 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv IDquant-ph/0012036 (version 2)
Pith IDKHTUZTHE, Pith's permanent record of this paper and its review
CitationG.Giachetta, G.Sardanashvily, L.Mangiarotti. "Covariant geometric quantization of non-relativistic Hamiltonian mechanics." arXiv:quant-ph/0012036 (2000). https://pith.science/paper/KHTUZTHE
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,234 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.15 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. contribution 1.00 0.94 0.12 asserted 1.00
s1 This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. background 0.88 0.15 0.04 asserted 1.00
s2 The goal is the Schrodinger representation of V^*Q. contribution 0.66 0.22 0.06 asserted 0.72
s3 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. result 0.90 0.91 0.52 asserted 1.00
s4 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. result 0.50 0.84 0.32 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.89 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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