dorsal/arxiv
View SchemaEffective Quantum Observables
| Authors | N. Brunner, K. Svozil, M. Baaz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9501018 |
| URL | https://arxiv.org/abs/quant-ph/9501018 |
| DOI | 10.1007/BF02849839 |
| Journal | NuovoCim.B110:1397-1414,1995 |
Abstract
Thought experiments about the physical nature of set theoretical counterexamples to the axiom of choice motivate the investigation of peculiar constructions, e.g. an infinite dimensional Hilbert space with a modular quantum logic. Applying a concept due to BENIOFF, we identify the intrinsically effective Hamiltonians with those observables of quantum theory which may coexist with a failure of the axiom of choice. Here a self adjoint operator is intrinsically effective, iff the Schroedinger equation of its generated semigroup is soluble by means of eigenfunction series expansions.
{
"annotation_id": "40bfcf84-2e3f-484a-aac1-612209eb81d5",
"date_created": "2026-03-02T18:02:37.271000Z",
"date_modified": "2026-03-02T18:02:37.271000Z",
"file_hash": "508feddba7575da5bb08cf3162e9060fa59c32fa1bf1bca21002155a5d9e9256",
"private": false,
"record": {
"abstract": "Thought experiments about the physical nature of set theoretical\ncounterexamples to the axiom of choice motivate the investigation of peculiar\nconstructions, e.g. an infinite dimensional Hilbert space with a modular\nquantum logic. Applying a concept due to BENIOFF, we identify the intrinsically\neffective Hamiltonians with those observables of quantum theory which may\ncoexist with a failure of the axiom of choice. Here a self adjoint operator is\nintrinsically effective, iff the Schroedinger equation of its generated\nsemigroup is soluble by means of eigenfunction series expansions.",
"arxiv_id": "quant-ph/9501018",
"authors": [
"N. Brunner",
"K. Svozil",
"M. Baaz"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/BF02849839",
"journal_ref": "NuovoCim.B110:1397-1414,1995",
"title": "Effective Quantum Observables",
"url": "https://arxiv.org/abs/quant-ph/9501018"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "7a966e5f-c7ba-4a23-a8a6-1a0054b9a0e5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}