dorsal/arxiv
View SchemaComment on ``Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty''
| Authors | D. C. Latimer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603259 |
| URL | https://arxiv.org/abs/quant-ph/0603259 |
| DOI | 10.1103/PhysRevA.75.066101 |
| Journal | Phys. Rev. A 75, 066101 (2007) |
Abstract
In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del Castillo consider various symplectic structures on the classical phase space of the two-dimensional isotropic harmonic oscillator. Using Dirac's quantization condition, the authors investigate how these alternative symplectic forms affect this system's quantization. They claim that these symplectic structures result in mutually inequivalent quantum theories. In fact, we show here that there exists a unitary map between the two representation spaces so that the various quantizations are equivalent.
{
"annotation_id": "c44db7f5-5c7c-4bdd-9f58-921ba6c1751e",
"date_created": "2026-03-02T18:02:26.464000Z",
"date_modified": "2026-03-02T18:02:26.464000Z",
"file_hash": "732abc156f02624bc2b96aa5c9bdda4015906a781e589cb23440865910578016",
"private": false,
"record": {
"abstract": "In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del\nCastillo consider various symplectic structures on the classical phase space of\nthe two-dimensional isotropic harmonic oscillator. Using Dirac\u0027s quantization\ncondition, the authors investigate how these alternative symplectic forms\naffect this system\u0027s quantization. They claim that these symplectic structures\nresult in mutually inequivalent quantum theories. In fact, we show here that\nthere exists a unitary map between the two representation spaces so that the\nvarious quantizations are equivalent.",
"arxiv_id": "quant-ph/0603259",
"authors": [
"D. C. Latimer"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.066101",
"journal_ref": "Phys. Rev. A 75, 066101 (2007)",
"title": "Comment on ``Symplectic quantization, inequivalent quantum theories, and Heisenberg\u0027s principle of uncertainty\u0027\u0027",
"url": "https://arxiv.org/abs/quant-ph/0603259"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "94ad802d-4bf3-489d-9974-e548096788d8",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}