dorsal/arxiv
View Schema(p,q)-Sheaves and the Representability Problem
| Authors | A. I. Panin |
|---|---|
| Categories | |
| ArXiv ID | physics/0210070 |
| URL | https://arxiv.org/abs/physics/0210070 |
Abstract
General properties of new models of the electronic Fock spaces based on the notion of (p,q)-sheaves are studied. Interrelation between simple sheaves and density operators is established. Explicit expressions for the transformed reduced Hamiltonians in terms of the standard creation-annihilation operators are presented. General scheme of parametrization of p-electron states by k-electron means (k=2,3,...) is described and studied in detail for the case of sheaves induced by k-electron wavefunctions. It is demonstrated that under certain conditions p-electron problem may be reformulated as the eigenvalue problem in k-electron space equipped with certain p-electron metric. Simple numerical examples are given to illustrate our approach.
{
"annotation_id": "9c038aeb-ebeb-4248-a461-48507d66cdf0",
"date_created": "2026-03-02T18:00:43.485000Z",
"date_modified": "2026-03-02T18:00:43.485000Z",
"file_hash": "944f759f9b1c6a02e9120d984b9af337a3a07fe4c32552b1da956a2b854ab811",
"private": false,
"record": {
"abstract": "General properties of new models of the electronic Fock spaces based on the\nnotion of (p,q)-sheaves are studied. Interrelation between simple sheaves and\ndensity operators is established. Explicit expressions for the transformed\nreduced Hamiltonians in terms of the standard creation-annihilation operators\nare presented. General scheme of parametrization of p-electron states by\nk-electron means (k=2,3,...) is described and studied in detail for the case of\nsheaves induced by k-electron wavefunctions. It is demonstrated that under\ncertain conditions p-electron problem may be reformulated as the eigenvalue\nproblem in k-electron space equipped with certain p-electron metric. Simple\nnumerical examples are given to illustrate our approach.",
"arxiv_id": "physics/0210070",
"authors": [
"A. I. Panin"
],
"categories": [
"physics.chem-ph"
],
"title": "(p,q)-Sheaves and the Representability Problem",
"url": "https://arxiv.org/abs/physics/0210070"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "d85851cd-89fc-45cf-b793-2b1cd8ed7688",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}