dorsal/arxiv
View SchemaCanonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric
| Authors | J. C. Garrison, R. Y. Chiao |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406222 |
| URL | https://arxiv.org/abs/quant-ph/0406222 |
| DOI | 10.1103/PhysRevA.70.053826 |
Abstract
An ad hoc quantization scheme for the electromagnetic field in a weakly dispersive, transparent dielectric leads to the definition of canonical and kinetic forms for the momentum of the electromagnetic field in a dispersive medium. The canonical momentum is uniquely defined as the operator that generates spatial translations in a uniform medium, but the quantization scheme suggests two possible choices for the kinetic momentum operator, corresponding to the Abraham or the Minkowski momentum in classical electrodynamics. Another implication of this procedure is that a wave packet containing a single dressed photon travels at the group velocity through the medium. The physical significance of the canonical momentum has already been established by considerations of energy and momentum conservation in the atomic recoil due to spontaneous emission, the Cerenkov effect, the Doppler effect, and phase matching in nonlinear optical processes. In addition, the data of the Jones and Leslie radiation pressure experiment is consistent with the assignment of one ?k unit of canonical momentum to each dressed photon. By contrast, experiments in which the dielectric is rigidly accelerated by unbalanced electromagnetic forces require the use of the Abraham momentum.
{
"annotation_id": "91a23911-44e2-4677-b6a6-a32a90dced51",
"date_created": "2026-03-02T18:02:10.396000Z",
"date_modified": "2026-03-02T18:02:10.396000Z",
"file_hash": "e83fe09e07a0ba605f33cee900a1f83368b485c06ae825a37bd2126fb5f6a1ce",
"private": false,
"record": {
"abstract": "An ad hoc quantization scheme for the electromagnetic field in a weakly\ndispersive, transparent dielectric leads to the definition of canonical and\nkinetic forms for the momentum of the electromagnetic field in a dispersive\nmedium. The canonical momentum is uniquely defined as the operator that\ngenerates spatial translations in a uniform medium, but the quantization scheme\nsuggests two possible choices for the kinetic momentum operator, corresponding\nto the Abraham or the Minkowski momentum in classical electrodynamics. Another\nimplication of this procedure is that a wave packet containing a single dressed\nphoton travels at the group velocity through the medium. The physical\nsignificance of the canonical momentum has already been established by\nconsiderations of energy and momentum conservation in the atomic recoil due to\nspontaneous emission, the Cerenkov effect, the Doppler effect, and phase\nmatching in nonlinear optical processes. In addition, the data of the Jones and\nLeslie radiation pressure experiment is consistent with the assignment of one\n?k unit of canonical momentum to each dressed photon. By contrast, experiments\nin which the dielectric is rigidly accelerated by unbalanced electromagnetic\nforces require the use of the Abraham momentum.",
"arxiv_id": "quant-ph/0406222",
"authors": [
"J. C. Garrison",
"R. Y. Chiao"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.70.053826",
"title": "Canonical and kinetic forms of the electromagnetic momentum in an ad hoc quantization scheme for a dispersive dielectric",
"url": "https://arxiv.org/abs/quant-ph/0406222"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "91df18f0-8add-4013-b33a-c778163cbb0f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}