dorsal/arxiv
View SchemaCenter of the charged particle orbit for any linear gauge
| Authors | Wojciech Florek |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9801017 |
| URL | https://arxiv.org/abs/quant-ph/9801017 |
Abstract
In the case of a constant uniform magnetic field it can be assumed, without the loss of generality, that the vector potential (the gauge) is a linear function of position, i.e. it could be considered as a three-dimensional real matrix or, more generally in an n-dimensional space, as a tensor A of the rank two. The magnetic tensor H is obtained from A by antisymmetrization, i.e. H=A-A^T. It is shown that the transpose of A plays a special role, since it determines the operator of the orbit center of a charged particle moving in an external magnetic field H. Moreover, this movement can be considered as a combination of N<=n independent cyclotronic movements in orthogonal planes (cyclotron orbits) with quantized energies, whereas in other n-2N dimensions the particle is completely free with a continuous energy spectrum. The proposed approach enables introduction of the four-dimensional space-time and, after some generalizations, non-linear gauges.
{
"annotation_id": "da48c73f-efe0-423d-b1b2-3f142e38eafe",
"date_created": "2026-03-02T18:02:40.649000Z",
"date_modified": "2026-03-02T18:02:40.649000Z",
"file_hash": "9fa4e417e8285cca2009a84b0466bd9d3790482bac017334079585875fb24087",
"private": false,
"record": {
"abstract": "In the case of a constant uniform magnetic field it can be assumed, without\nthe loss of generality, that the vector potential (the gauge) is a linear\nfunction of position, i.e. it could be considered as a three-dimensional real\nmatrix or, more generally in an n-dimensional space, as a tensor A of the rank\ntwo. The magnetic tensor H is obtained from A by antisymmetrization, i.e.\nH=A-A^T. It is shown that the transpose of A plays a special role, since it\ndetermines the operator of the orbit center of a charged particle moving in an\nexternal magnetic field H. Moreover, this movement can be considered as a\ncombination of N\u003c=n independent cyclotronic movements in orthogonal planes\n(cyclotron orbits) with quantized energies, whereas in other n-2N dimensions\nthe particle is completely free with a continuous energy spectrum. The proposed\napproach enables introduction of the four-dimensional space-time and, after\nsome generalizations, non-linear gauges.",
"arxiv_id": "quant-ph/9801017",
"authors": [
"Wojciech Florek"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"math-ph",
"math.MP"
],
"title": "Center of the charged particle orbit for any linear gauge",
"url": "https://arxiv.org/abs/quant-ph/9801017"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "39feb2dd-073f-4109-9fd2-f106b9118cd9",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}