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On the quadratic Fock functor

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
External document link
http://arxiv.org/abs/0910.3350v1
Date
2012
Journal name
Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume
15
Number
2
Publisher
World Scientific
Publication identifier
Metadata
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Author(s)
Dhahri, Ameur
Abstract (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.
Subjects / Keywords
Heisenberg model; Hilbert spaces; Lie algebras