dorsal/arxiv
View SchemaThe role of phase space geometry in Heisenberg's uncertainty relation
| Authors | Charis Anastopoulos, Ntina Savvidou |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304049 |
| URL | https://arxiv.org/abs/quant-ph/0304049 |
| DOI | 10.1016/S0003-4916(03)00145-3 |
| Journal | Annals Phys. 308 (2003) 329-353 |
Abstract
Aiming towards a geometric description of quantum theory, we study the coherent states-induced metric on the phase space, which provides a geometric formulation of the Heisenberg uncertainty relations (both the position-momentum and the time-energy ones). The metric also distinguishes the original uncertainty relations of Heisenberg from the ones that are obtained from non-commutativity of operators. Conversely, the uncertainty relations can be written in terms of this metric only, hence they can be formulated for any physical system, including ones with non-trivial phase space. Moreover, the metric is a key ingredient of the probability structure of continuous-time histories on phase space. This fact allows a simple new proof the impossibility of the physical manifestation of the quantum Zeno and anti-Zeno paradoxes. Finally, we construct the coherent states for a spinless relativistic particle, as a non-trivial example by which we demonstrate our results.
{
"annotation_id": "ad92a158-2071-4988-b049-2df68f102d3b",
"date_created": "2026-03-02T18:01:58.859000Z",
"date_modified": "2026-03-02T18:01:58.859000Z",
"file_hash": "da33fd35d84ed284ab48277effabf7ead2a01defdae24d3410a4ba1bc70db77a",
"private": false,
"record": {
"abstract": "Aiming towards a geometric description of quantum theory, we study the\ncoherent states-induced metric on the phase space, which provides a geometric\nformulation of the Heisenberg uncertainty relations (both the position-momentum\nand the time-energy ones). The metric also distinguishes the original\nuncertainty relations of Heisenberg from the ones that are obtained from\nnon-commutativity of operators. Conversely, the uncertainty relations can be\nwritten in terms of this metric only, hence they can be formulated for any\nphysical system, including ones with non-trivial phase space. Moreover, the\nmetric is a key ingredient of the probability structure of continuous-time\nhistories on phase space. This fact allows a simple new proof the impossibility\nof the physical manifestation of the quantum Zeno and anti-Zeno paradoxes.\nFinally, we construct the coherent states for a spinless relativistic particle,\nas a non-trivial example by which we demonstrate our results.",
"arxiv_id": "quant-ph/0304049",
"authors": [
"Charis Anastopoulos",
"Ntina Savvidou"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1016/S0003-4916(03)00145-3",
"journal_ref": "Annals Phys. 308 (2003) 329-353",
"title": "The role of phase space geometry in Heisenberg\u0027s uncertainty relation",
"url": "https://arxiv.org/abs/quant-ph/0304049"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "910b94c7-901f-413f-8b74-5d42dd13cb4a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}