On the quadratic Fock functor

Ameur Dhahri (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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: Quadratic Fock space; quadratic second quantization; orthogonal projection

Domaines: Analyse fonctionnelle [math.FA]

Ameur Dhahri. On the quadratic Fock functor. 2009. ⟨hal-00424803⟩