Quadratic exponential vectors

Accardi, Luigi; Dhahri, Ameur

Accardi, Luigi; Dhahri, Ameur (2009), Quadratic exponential vectors, Journal of Mathematical Physics, 50, 12, p. Paper 122103. http://dx.doi.org/10.1063/1.3266166

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/0910.2453v1

Date

2009

Journal name

Journal of Mathematical Physics

Volume

Number

Publisher

American Institute of Physics

Pages

Paper 122103

Abstract (EN)

We give a necessary and sufficient condition for the existence of a quadratic exponential vector with test function in L2(mathd)∩L∞(mathd). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique different from the one used by Accardi et al. [Quantum Probability and Infinite Dimensional Analysis, Vol. 25, p. 262, (2009)] , we also extend, to a more general class of test functions, the explicit form of the scalar product between two such vectors.

Subjects / Keywords

integral equations; Lie algebras; quantisation (quantum theory); vectors