dorsal/arxiv
View SchemaQuantum-Mechanical Dualities on the Torus
| Authors | J. M. Isidro |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310158 |
| URL | https://arxiv.org/abs/quant-ph/0310158 |
| DOI | 10.1142/S0217732304014860 |
| Journal | Mod.Phys.Lett. A19 (2004) 1733-1744 |
Abstract
On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e., independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments suggest that the notion of a quantum may not be universal. Transformations between observers that do not agree on the notion of an elementary quantum are called dualities. Classical phase spaces admitting more than one complex-differentiable structure thus provide a natural framework to study dualities in quantum mechanics. As an example we quantise a classical mechanics whose phase space is a torus and prove explicitly that it exhibits dualities.
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"abstract": "On classical phase spaces admitting just one complex-differentiable\nstructure, there is no indeterminacy in the choice of the creation operators\nthat create quanta out of a given vacuum. In these cases the notion of a\nquantum is universal, i.e., independent of the observer on classical phase\nspace. Such is the case in all standard applications of quantum mechanics.\nHowever, recent developments suggest that the notion of a quantum may not be\nuniversal. Transformations between observers that do not agree on the notion of\nan elementary quantum are called dualities. Classical phase spaces admitting\nmore than one complex-differentiable structure thus provide a natural framework\nto study dualities in quantum mechanics. As an example we quantise a classical\nmechanics whose phase space is a torus and prove explicitly that it exhibits\ndualities.",
"arxiv_id": "quant-ph/0310158",
"authors": [
"J. M. Isidro"
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"doi": "10.1142/S0217732304014860",
"journal_ref": "Mod.Phys.Lett. A19 (2004) 1733-1744",
"title": "Quantum-Mechanical Dualities on the Torus",
"url": "https://arxiv.org/abs/quant-ph/0310158"
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