Résumé en anglais

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.