dorsal/arxiv
View SchemaHamiltonian Systems on Complex Grassmann Manifold. Holonomy and Schrodinger Equation
| Authors | Zakaria Giunashvili |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209141 |
| URL | https://arxiv.org/abs/quant-ph/0209141 |
Abstract
Differential geometric structures such as the principal bundle for the canonical vector bundle on a complex Grassmann manifold, the canonical connection form on this bundle, the canonical symplectic form on a complex Grassmann manifold and the corresponding dynamical systems are investigated. The Grassmann manifold is considered as an orbit of the co-adjoint action and the symplectic form is described as the restriction of the canonical Poisson structure on a Lie coalgebra. The holonomy of the connection on the principal bundle over Grassmannian and its relation with Berry phase is considered and investigated for the integral curves of Hamiltonian dynamical systems.
{
"annotation_id": "4c5c98e0-9522-44d3-ae14-1eb128cbb17e",
"date_created": "2026-03-02T18:01:52.976000Z",
"date_modified": "2026-03-02T18:01:52.976000Z",
"file_hash": "31d43bfceb60016028ad118a1b93d6273d90af25c4bea4176d6a4e9595514802",
"private": false,
"record": {
"abstract": "Differential geometric structures such as the principal bundle for the\ncanonical vector bundle on a complex Grassmann manifold, the canonical\nconnection form on this bundle, the canonical symplectic form on a complex\nGrassmann manifold and the corresponding dynamical systems are investigated.\nThe Grassmann manifold is considered as an orbit of the co-adjoint action and\nthe symplectic form is described as the restriction of the canonical Poisson\nstructure on a Lie coalgebra. The holonomy of the connection on the principal\nbundle over Grassmannian and its relation with Berry phase is considered and\ninvestigated for the integral curves of Hamiltonian dynamical systems.",
"arxiv_id": "quant-ph/0209141",
"authors": [
"Zakaria Giunashvili"
],
"categories": [
"quant-ph"
],
"title": "Hamiltonian Systems on Complex Grassmann Manifold. Holonomy and Schrodinger Equation",
"url": "https://arxiv.org/abs/quant-ph/0209141"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "c1adf7fc-59ac-4fc8-bedb-ab05670500f2",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}