dorsal/arxiv
View SchemaUniqueness of conserved currents in quantum mechanics
| Authors | Peter Holland |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0305175 |
| URL | https://arxiv.org/abs/quant-ph/0305175 |
| DOI | 10.1002/andp.200310022 |
| Journal | Ann. Phys. (Leipzig) 12, 446-62 (2003) (slightly modified version) |
Abstract
It is proved by a functional method that the conventional expression for the Dirac current is the only conserved 4-vector implied by the Dirac equation that is a function of just the quantum state. The demonstration is extended to derive the unique conserved currents implied by the coupled Maxwell-Dirac equations and the Klein-Gordon equation. The uniqueness of the usual Pauli and Schrodinger currents follows by regarding these as the non-relativistic limits of the Dirac and Klein-Gordon currents, respectively. The existence and properties of further conserved vectors that are not functions of just the state is examined.
{
"annotation_id": "889833c9-f5eb-4a2c-a2a6-45cff528cecb",
"date_created": "2026-03-02T18:02:00.141000Z",
"date_modified": "2026-03-02T18:02:00.141000Z",
"file_hash": "29826896a44fc737dc9d1e45b0a6869d0f05253ee096cb9ccc9d0785b0cfe375",
"private": false,
"record": {
"abstract": "It is proved by a functional method that the conventional expression for the\nDirac current is the only conserved 4-vector implied by the Dirac equation that\nis a function of just the quantum state. The demonstration is extended to\nderive the unique conserved currents implied by the coupled Maxwell-Dirac\nequations and the Klein-Gordon equation. The uniqueness of the usual Pauli and\nSchrodinger currents follows by regarding these as the non-relativistic limits\nof the Dirac and Klein-Gordon currents, respectively. The existence and\nproperties of further conserved vectors that are not functions of just the\nstate is examined.",
"arxiv_id": "quant-ph/0305175",
"authors": [
"Peter Holland"
],
"categories": [
"quant-ph"
],
"doi": "10.1002/andp.200310022",
"journal_ref": "Ann. Phys. (Leipzig) 12, 446-62 (2003) (slightly modified version)",
"title": "Uniqueness of conserved currents in quantum mechanics",
"url": "https://arxiv.org/abs/quant-ph/0305175"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "6af2322d-899c-4ce5-b319-f8f0ff62cc6a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}