dorsal/arxiv
View SchemaThe Frobenius formalism in Galois quantum systems
| Authors | A. Vourdas |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605054 |
| URL | https://arxiv.org/abs/quant-ph/0605054 |
| DOI | 10.1007/s10440-006-9040-7 |
| Journal | Acta Applicandae Mathematicae 93 (2006) 197-214 |
Abstract
Quantum systems in which the position and momentum take values in the ring ${\cal Z}_d$ and which are described with $d$-dimensional Hilbert space, are considered. When $d$ is the power of a prime, the position and momentum take values in the Galois field $GF(p^ \ell)$, the position-momentum phase space is a finite geometry and the corresponding `Galois quantum systems' have stronger properties. The study of these systems uses ideas from the subject of field extension in the context of quantum mechanics. The Frobenius automorphism in Galois fields leads to Frobenius subspaces and Frobenius transformations in Galois quantum systems. Links between the Frobenius formalism and Riemann surfaces, are discussed.
{
"annotation_id": "b88598ff-6a94-4212-b775-968324b9245c",
"date_created": "2026-03-02T18:02:27.644000Z",
"date_modified": "2026-03-02T18:02:27.644000Z",
"file_hash": "47a0952fc0185896c108233f0fe62db6848b00fe1de6d851304a62251da1199d",
"private": false,
"record": {
"abstract": "Quantum systems in which the position and momentum take values in the ring\n${\\cal Z}_d$ and which are described with $d$-dimensional Hilbert space, are\nconsidered. When $d$ is the power of a prime, the position and momentum take\nvalues in the Galois field $GF(p^ \\ell)$, the position-momentum phase space is\na finite geometry and the corresponding `Galois quantum systems\u0027 have stronger\nproperties. The study of these systems uses ideas from the subject of field\nextension in the context of quantum mechanics. The Frobenius automorphism in\nGalois fields leads to Frobenius subspaces and Frobenius transformations in\nGalois quantum systems. Links between the Frobenius formalism and Riemann\nsurfaces, are discussed.",
"arxiv_id": "quant-ph/0605054",
"authors": [
"A. Vourdas"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s10440-006-9040-7",
"journal_ref": "Acta Applicandae Mathematicae 93 (2006) 197-214",
"title": "The Frobenius formalism in Galois quantum systems",
"url": "https://arxiv.org/abs/quant-ph/0605054"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "85c60d68-2497-4d6f-a8dd-f849a69d4212",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}