On the quadratic Fock functor

Dhahri, Ameur

Dhahri, Ameur (2012), On the quadratic Fock functor, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 15, 2. http://dx.doi.org/10.1142/S0219025712500129

Type

Article accepté pour publication ou publié

Lien vers un document non conservé dans cette base

http://arxiv.org/abs/0910.3350v1

Date

2012

Nom de la revue

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volume

Numéro

Éditeur

World Scientific

Résumé (EN)

We prove that the quadratic second quantization of an operator p on $L^2(\mathbb{R}^d)\cap L^\infty (\mathbb{R}^d)$ is an orthogonal projection on the quadratic Fock space if and only if p =MI, where MI is a multiplication operator by a characteristic function I.

Mots-clés

Heisenberg model; Hilbert spaces; Lie algebras