dorsal/arxiv
View SchemaOn Galilei Invariance in Quantum Mechanics and the Bargmann Superselection Rule
| Authors | Domenico Giulini |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9508002 |
| URL | https://arxiv.org/abs/quant-ph/9508002 |
| DOI | 10.1006/aphy.1996.0069 |
| Journal | Annals Phys. 249 (1996) 222-235 |
Abstract
We reinvestigate Bargmann's superselection rule for the overall mass of $n$ particles in ordinary quantum mechanics with Galilei invariant interaction potential. We point out that in order for mass to define a superselection rule it should be considered as a dynamical variable. We present a minimal extension of the original dynamics in which mass it treated as dynamical variable. Here the classical symmetry group turns out to be given by an $\reals$-extension of the Galilei group which formerly appeared only at the quantum level. There is now no obstruction to implement an action of the classical symmetry group on Hilbert space. We include some critical comments of a general nature on formal derivations of superselection rules without dynamical context.
{
"annotation_id": "594e096e-057f-4ef3-a1e5-5287ab33b5e3",
"date_created": "2026-03-02T18:02:38.016000Z",
"date_modified": "2026-03-02T18:02:38.016000Z",
"file_hash": "3e95b48f4c4813dcbb735e4a986aebd37b14a2128fed1a73c948115d441298e7",
"private": false,
"record": {
"abstract": "We reinvestigate Bargmann\u0027s superselection rule for the overall mass of $n$\nparticles in ordinary quantum mechanics with Galilei invariant interaction\npotential. We point out that in order for mass to define a superselection rule\nit should be considered as a dynamical variable. We present a minimal extension\nof the original dynamics in which mass it treated as dynamical variable. Here\nthe classical symmetry group turns out to be given by an $\\reals$-extension of\nthe Galilei group which formerly appeared only at the quantum level. There is\nnow no obstruction to implement an action of the classical symmetry group on\nHilbert space. We include some critical comments of a general nature on formal\nderivations of superselection rules without dynamical context.",
"arxiv_id": "quant-ph/9508002",
"authors": [
"Domenico Giulini"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1006/aphy.1996.0069",
"journal_ref": "Annals Phys. 249 (1996) 222-235",
"title": "On Galilei Invariance in Quantum Mechanics and the Bargmann Superselection Rule",
"url": "https://arxiv.org/abs/quant-ph/9508002"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "38f0a43f-5f40-4721-81af-49d475d371cb",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}