# Geometry of quantum active subspaces and of effective Hamiltonians

## Abstract

We propose a geometric formulation of the theory of effective Hamiltonians associated with active spaces. We analyze particularly the case of the time-dependent wave operator theory. This formulation is related to the geometry of the manifold of the active spaces, particularly to its Kaehlerian structure. We introduce the concept of quantum distance between active spaces. We show that the time-dependent wave operator theory is, in fact, a gauge theory, and we analyze its relationship with the geometric phase concept.

- Authors:

- Observatoire de Besancon, Institut UTINAM (CNRS UMR 6213), 41bis Avenue de l'Observatoire, BP1615, 25010 Besancon Cedex (France)

- Publication Date:

- OSTI Identifier:
- 20929699

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 5; Other Information: DOI: 10.1063/1.2723552; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; GAUGE INVARIANCE; GEOMETRY; HAMILTONIANS; QUANTUM FIELD THEORY; SCHROEDINGER EQUATION; TIME DEPENDENCE

### Citation Formats

```
Viennot, David.
```*Geometry of quantum active subspaces and of effective Hamiltonians*. United States: N. p., 2007.
Web. doi:10.1063/1.2723552.

```
Viennot, David.
```*Geometry of quantum active subspaces and of effective Hamiltonians*. United States. doi:10.1063/1.2723552.

```
Viennot, David. Tue .
"Geometry of quantum active subspaces and of effective Hamiltonians". United States.
doi:10.1063/1.2723552.
```

```
@article{osti_20929699,
```

title = {Geometry of quantum active subspaces and of effective Hamiltonians},

author = {Viennot, David},

abstractNote = {We propose a geometric formulation of the theory of effective Hamiltonians associated with active spaces. We analyze particularly the case of the time-dependent wave operator theory. This formulation is related to the geometry of the manifold of the active spaces, particularly to its Kaehlerian structure. We introduce the concept of quantum distance between active spaces. We show that the time-dependent wave operator theory is, in fact, a gauge theory, and we analyze its relationship with the geometric phase concept.},

doi = {10.1063/1.2723552},

journal = {Journal of Mathematical Physics},

number = 5,

volume = 48,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2723552

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